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Intersectplot line quality ...

Asked by: Ronan 1341
plotting intersectplot
June 10 2024
1  3

I am using intersectplot  to make projective coordinate plots. Everything intersects the plane z=1. I find the plot quality poor, i.e. dotty dashy lines and circle. This seem to be the best linestyle=solid can do here. gridrefine can't be applied here. 
Any suggestions to improve quality here?
Maybe intersectplot is not the best aprroach here but so far it is all if have figured out.


> 

restart
> 

 

> 

 

> 

with(plottools)

[annulus, arc, arrow, circle, colorbar, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, polygonbyname, prism, project, pyramid, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate, triangulate]

 (1)
> 

with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

 (2)
> 

 

> 

 

> 

DistCircle:=x^2+y^2=1

x^2+y^2 = 1

 (3)
> 

pt1:=[1/4,3/4]

[1/4, 3/4]

 (4)
> 

pt2:=[7/8,-1/3]

[7/8, -1/3]

 (5)
> 

pt3:=[-3/2,3/7]

[-3/2, 3/7]

 (6)
> 

pt4:=[3/5,-4/5]

[3/5, -4/5]

 (7)
> 

pt5:=[-1/10,-3/2]

[-1/10, -3/2]

 (8)
> 

 

> 

L12:=-(13*x)/12 - (5*y)/8 + 71/96; #LnPeqns(pt1,pt2);

-(13/12)*x-(5/8)*y+71/96

 (9)
> 

L13:=-(9*x)/28 + (7*y)/4 - 69/56; #LnPeqns(pt1,pt3);

-(9/28)*x+(7/4)*y-69/56

 (10)
> 

L23:=(16*x)/21 + (19*y)/8 + 1/8; #LnPeqns(pt2,pt3);

(16/21)*x+(19/8)*y+1/8

 (11)
> 

L35:=(27*x)/14 + (7*y)/5 + 321/140; #LnPeqns(pt5,pt3)

(27/14)*x+(7/5)*y+321/140

 (12)
> 

nullline:=3/5*x-4/5*y-1

(3/5)*x-(4/5)*y-1

 (13)
> 

ptplt:=point([pt1,pt2,pt3,pt4,pt5],color="Green",symbol=solidcircle,symbolsize=10):
txtplt:=textplot([pt4[],typeset("pt4")],align={below,right}):
> 

plt1:=display(txtplt,implicitplot([DistCircle,L12,L13,L23,L35,nullline],x=-2..2,y=-1.5...1.5,color=[red,blue,blue,blue,blue,cyan]),ptplt,scaling=constrained)
> 

 

 
> 

# Projective Geometry Version
> 

DistCirclez:=x^2+y^2-z^2;  #a Cone
> 

 

x^2+y^2-z^2

 (14)
> 

pt1p:=[pt1[],1];
pt2p:=[pt2[],1];
pt3p:=[pt3[],1];
pt4p:=[pt4[],1];
pt5p:=[pt5[],1];

[1/4, 3/4, 1]

  

[7/8, -1/3, 1]

  

[-3/2, 3/7, 1]

  

[3/5, -4/5, 1]

  

[-1/10, -3/2, 1]

 (15)
> 

 

> 

 

> 

 

> 

L12p:=(13*x)/12 + (5*y)/8 - (71*z)/96;#LnPeqns([pt1p,pt2p,[0,0,0]]);

(13/12)*x+(5/8)*y-(71/96)*z

 (16)
> 

L13p:=(13*x)/12 + (5*y)/8 - (71*z)/96;#LnPeqns([pt1p,pt3p,[0,0,0]]);

(13/12)*x+(5/8)*y-(71/96)*z

 (17)
> 

L23p:=(9*x)/28 - (7*y)/4 + (69*z)/56;#LnPeqns([pt2p,pt3p,[0,0,0]]);

(9/28)*x-(7/4)*y+(69/56)*z

 (18)
> 

L35p:=(27*x)/14 + (7*y)/5 + (321*z)/140;#LnPeqns([pt3p,pt5p,[0,0,0]]);

(27/14)*x+(7/5)*y+(321/140)*z

 (19)
> 

L04p:=3/5*x-4/5*y-1*z;

(3/5)*x-(4/5)*y-z

 (20)
> 

ptpltp:=point([pt1p,pt2p,pt3p,pt4p,pt5p],symbol=solidsphere, symbolsize=8,color="green"):
intp1:=intersectplot(DistCirclez,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,linestyle=solid):#unit circle at z=1
intp12p:=intersectplot(L12p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp13p:=intersectplot(L13p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp23p:=intersectplot(L23p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp35p:=intersectplot(L35p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp04p:=intersectplot(L04p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=cyan):
> 

 
> 

display(ptpltp,intp1,intp12p,intp13p,intp23p,intp35p,intp04p,scaling=constrained,caption="Projective Co-ords on plane z=1",axes=normal,axis[3]=[tickmarks=[1]])

 
> 

 


Download 2024-06-10_Q_Intersectplot_quality.mw

examples of hard ode solutions to show they satisf...

Asked by: nm 11353
ode differential-equations odetest
June 09 2024
1  3

These are two examples of challenging ode solutions to show they satisfy the ode.

I tried many things myself but can't do it. Feel free to use any method or trick you want. The goal is simply to show that the solution is correct. The solutions are correct as far as I know, but hard to show by back substitution since the solutions are given in form of integrals and RootOf in them.

Extra credit points will be awarded for those who manage to do both.

28148

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Example 1

 
> 

_EnvTry:='hard';
ode:=y(x) = arcsin(diff(y(x), x)) + ln(1 + diff(y(x), x)^2);
sol:=dsolve(ode);
r:=odetest(sol,ode);
coulditbe(r=0);

hard

y(x) = arcsin(diff(y(x), x))+ln(1+(diff(y(x), x))^2)

x-Intat(1/sin(RootOf(-_a+_Z+ln(sin(_Z)^2+1))), _a = y(x))-c__1 = 0

-arcsin(sin(RootOf(-y(x)+_Z+ln(3/2-(1/2)*cos(2*_Z)))))+RootOf(-y(x)+_Z+ln(3/2-(1/2)*cos(2*_Z)))

FAIL

Example 2

 
> 

ode:=(1 + diff(y(x), x)^2)*(arctan(diff(y(x), x)) + a*x) + diff(y(x), x) = 0;
sol:=dsolve(ode);
r:=odetest(sol,ode);
coulditbe(r=0)

(1+(diff(y(x), x))^2)*(arctan(diff(y(x), x))+a*x)+diff(y(x), x) = 0

y(x) = Int(tan(RootOf(a*x*tan(_Z)^2+tan(_Z)^2*_Z+a*x+tan(_Z)+_Z)), x)+c__1

(-arctan(tan(RootOf(2*a*x+sin(2*_Z)+2*_Z)))+RootOf(2*a*x+sin(2*_Z)+2*_Z))*tan(RootOf(2*a*x+sin(2*_Z)+2*_Z))/(a*x+RootOf(2*a*x+sin(2*_Z)+2*_Z))

FAIL

 

 

Download showing_solution_satisfies_ode.mw

Is there a way to create the BoxPlot using 2 list...

Asked by: jalal 435
plotting statistics boxplot
June 09 2024
0  3

Hi,

I am exploring the boxplot, and I see that I do not have the option to integrate 2 lists: One for observations and one for frequencies. The BoxPlot command only accepts one list (List A in my example). Is there a way to create the BoxPlot using the 'Obs' and 'Eff' lists? Thank you for your insight

QBoxPlot.mw

simplifying a/sqrt(tan(x+c__1)^2+1);...

Asked by: nm 11353
simplify simplification trig
June 09 2024
2  10

How to make Maple simplify a/sqrt(tan(x+c__1)^2+1); to a/sqrt(sec(x+c__1)^2);  ?

Below is worksheet. since the second one is smaller in leaf size, expected simplify(...,size) to do it, But it did not. Any suggestions?

24832

> 

LC:=MmaTranslator:-Mma:-LeafCount;
e1:=a/sqrt(tan(x+c__1)^2+1);
e2:=a/sqrt(sec(x+c__1)^2);

MmaTranslator:-Mma:-LeafCount

a/(tan(x+c__1)^2+1)^(1/2)

a/(sec(x+c__1)^2)^(1/2)

> 

LC(e1);

12

> 

LC(e2);

10

> 

#we see they are same
simplify(e1-e2);

0

> 

#both nothing below make e1 to e2
simplify(e1); #not good simplification at all. Adds csgn.
LC(%);

a*csgn(sec(x+c__1))*cos(x+c__1)

11

> 

#expected this to do it but no
simplify(e1,size);
LC(%);

a/(tan(x+c__1)^2+1)^(1/2)

12

> 

simplify(e1,trig);

a/(tan(x+c__1)^2+1)^(1/2)

> 

combine(e1,trig);

a/(tan(x+c__1)^2+1)^(1/2)

> 

 


Using some other software:

 

 

 

Download tan_sec_simplification_june_9_2024.mw

Where is the code that simplifies this ...

Asked by: janhardo 700
programming simplification
June 08 2024
1  43

Can't figure out what code makes this simplification.
If this simplification works, it will be a part of a larger simplication procedure ( if it not conflicts hopefully) 
vereenvouding_hoe_-vraag_MPF.mw

PDEtools:-Solve vs. solve. RootOf form difference...

Asked by: nm 11353
solve differential-equations pdetools
June 08 2024
1  4

I was trying to find out why my solution was not validating for this ode. It turned out because I was using solve instead of PDEtools:-Solve. It took me sometime to find this.

This made huge difference on odetest to verify the solution.

This is very simple ode. We just need to integrate once. But first we have to solve for y'(x). 

And here comes the difference. When I used solve to solve for y'(x), odetest did not verify the solution.

When using PDEtools:-Solve, it did.

The difference is how each returned the solution for y'(x). Both have RootOf but written differently and this made the difference.

1) Why solutions are written differently? 

2) Is this to be expected? I have thought Solve uses same engine as solve below the cover.

3) is it possible to make solve give the same form as Solve or change to that form?

I am now changing more of my code to use PDEtools:-Solve because of this.

27860

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1757. The version installed in this computer is 1756 created 2024, June 5, 19:39 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

Using solve

 
> 

restart;

27860

> 

ode:=x-ln(diff(y(x),x))-sin(diff(y(x),x))=0;
RHS:=solve(ode,diff(y(x),x));

x-ln(diff(y(x), x))-sin(diff(y(x), x)) = 0

RootOf(_Z-exp(-sin(_Z)+x))

> 

mysol:= y(x) = Int(RHS,x)+c__1;

y(x) = Int(RootOf(_Z-exp(-sin(_Z)+x)), x)+c__1

> 

odetest(mysol,ode);

-ln(RootOf(_Z-exp(-sin(_Z)+x)))+x-sin(RootOf(_Z-exp(-sin(_Z)+x)))

using PDEtools:-Solve (now it verifies) with no extra effort

 
> 

restart;

27860

> 

ode:=x-ln(diff(y(x),x))-sin(diff(y(x),x))=0;
RHS:=PDEtools:-Solve(ode,diff(y(x),x)):
RHS:=rhs(%);

x-ln(diff(y(x), x))-sin(diff(y(x), x)) = 0

RootOf(-x+ln(_Z)+sin(_Z))

> 

mysol:= y(x) = Int(RHS,x)+c__1;

y(x) = Int(RootOf(-x+ln(_Z)+sin(_Z)), x)+c__1

> 

odetest(mysol,ode);

0

 

 

Download PDEtools_Solve_vs_solve_june_8_2024.mw

 

Update

Here is a counter example. Where now it is the other way around.

Using solve makes odetest happy, but when using PDEtools:-Solve odetest does not verify the solution.  Same exact ODE.   


 

28652

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1757 and is the same as the version installed in this computer, created 2024, June 6, 14:53 hours Pacific Time.`

Example, using solve works

 
> 

ode:=exp(diff(y(x), x) - y(x)) - diff(y(x), x)^2 + 1 = 0;
RHS:=solve(ode,diff(y(x),x));
RHS:=eval(RHS,y(x)=y);
mysol:=Intat(eval(1/RHS,y=_a),_a=y(x))=x+c__1;
odetest(mysol,ode);

exp(diff(y(x), x)-y(x))-(diff(y(x), x))^2+1 = 0

Warning, solutions may have been lost

RootOf(-exp(_Z-y(x))+_Z^2-1)

RootOf(-exp(_Z-y)+_Z^2-1)

Intat(1/RootOf(-exp(_Z-_a)+_Z^2-1), _a = y(x)) = x+c__1

0

Example, using PDEtools:-Solve fails

 
> 

ode:=exp(diff(y(x), x) - y(x)) - diff(y(x), x)^2 + 1 = 0;
RHS:=rhs(PDEtools:-Solve(ode,diff(y(x),x)));
RHS:=eval(RHS,y(x)=y);
mysol:=Intat(eval(1/RHS,y=_a),_a=y(x))=x+c__1;
odetest(mysol,ode);

exp(diff(y(x), x)-y(x))-(diff(y(x), x))^2+1 = 0

RootOf(_Z^2*exp(y(x))-exp(_Z)-exp(y(x)))

RootOf(_Z^2*exp(y)-exp(_Z)-exp(y))

Intat(1/RootOf(_Z^2*exp(_a)-exp(_Z)-exp(_a)), _a = y(x)) = x+c__1

exp(RootOf(_Z^2*exp(y(x))-exp(_Z)-exp(y(x)))-y(x))-RootOf(_Z^2*exp(y(x))-exp(_Z)-exp(y(x)))^2+1

> 

 


 

Download PDEtools_Solve_vs_solve_june_9_2024.mw

So now I have no idea which to use. Sometimes solve works and sometimes Solve works. I  guess I have to now solve the ode both ways each time and see which works.

 

why print shows nothing when Matrix is empty?...

Asked by: nm 11353
matrix print
June 07 2024
1  2

Should not  print("my matrix is ",A) at least print "my matrix is " even if A is not correctly filled/setup?

Notice that nothing shows on screen when using print (but lprint does)

Is this expected? If it makes any difference, I am using worksheet and this is my display options

21836

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

A:=Matrix(1,0);
> 

print("My matrix is =",A);
> 

lprint("My matrix is =",A);

"My matrix is =", Matrix(1,0,{},datatype = anything,storage = rectangular,order
= Fortran_order,shape = [])

 

 

Download why_print_empty_june_7_2024.mw

Result of odetest changes depending on previous c...

Asked by: nm 11353
differential-equations odetest
June 06 2024
2  1

If I do    odetest(...,odeA) I get correct result. But if I do    odetest(...,odeB);  odetest(...,odeA);   now it gives wrong output for the odeA one. 

Same exact code. It just depends on the call done before it.

Why would issuing a command before changes the output of odetest? It seems Maple remembers something from last call. But I have no idea how to fix this.

Is there a way to tell odetest not to remember or cache any results from last calls? i.e. Can I clear its remember table before calling odetest??

This is messing all my testing now since I get different result each time depending on which call was made before. I can't do restart before testing each ode, since this is done in a loop.  I just need a way to tell Maple to clear its internal cache so that each call to odetest is not affected by last call result. 

Doing forget(odetest); before the call had no effect.

Reported to Maplesoft.

Worksheet below

``

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

restart;

4556

> 

#EXAMPLE 1
ode:=x*diff(y(x),x)^n=0;
sol:=dsolve(ode);
odetest(sol,ode);

x*(diff(y(x), x))^n = 0

y(x) = c__1

0

> 

restart;

4556

> 

ode:=diff(y(x),x)^n=0;
sol:=dsolve(ode);
odetest(sol,ode);

(diff(y(x), x))^n = 0

y(x) = c__1

0^n

> 

##EXAMPLE 1 repeated. Why now different result??

ode:=x*diff(y(x),x)^n=0;
sol:=dsolve(ode);
odetest(sol,ode);

x*(diff(y(x), x))^n = 0

y(x) = c__1

x*0^n

Download why_different_result_from_odetest_june_6_2024.mw

Update

FYI, I got email from Maplesupport that Maple R&D group will look at this issue.

So hopefully this will be fixed in a future version of Maple.  

I am not able to find a workaround but doing tracing I see that odetest does rememebr something from last call but have no idea to fix this myself.

why this patmatch fails inside proc but works outs...

Asked by: nm 11353
programming patmatch
June 06 2024
1  1

I can't figure this out. Same exact patmatch works in global worksheet. But fails inside a proc.

I am using same exact code. In proc, I am doing    a::anything where `a` is now local symbol ofcourse. In worksheet, it is global ofcourse. I make sure I clear `a` in worksheet each time also.

So why it pathmatch fail in the proc? I must be doing something wrong but do not see it.,
 

26148

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

restart;

26148

> 

a:='a':
stat:=0^n:
> 

if patmatch(stat,0^a::anything) then
     0;
  else
     stat;
  fi;

0

> 

foo:=proc(stat)
  local a;
  if patmatch(stat,0^a::anything) then
     0;
  else
     stat;
  fi;
end proc:
> 

#why this does not return zero as expected?
foo(stat)

0^n

> 

 


Here is screen shot in debugger showing patmatch failed inside the proc

 

Very strange. What do I need to change in the proc to make it work as in worksheet? 

Download patmatch_in_proc.mw

strange odetest result. Is this valid?...

Asked by: nm 11353
ode differential-equations odetest
June 06 2024
3  3

Is the following valid result from odetest? is returns 0^n when 0 was expected.

Is this a bug or valid result? Maple solution is correct, so I expected 0 only not 0^n as result.

25748

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1756 and is the same as the version installed in this computer, created 2024, June 5, 19:39 hours Pacific Time.`

> 

ode:=diff(y(x), x)^n = 0

(diff(y(x), x))^n = 0

> 

sol:=dsolve(ode)

y(x) = c__1

> 

odetest(sol,ode)

0^n

> 

odetest(sol,ode) assuming n::real

0^n

> 

odetest(sol,ode) assuming n>0

0^n

 

 

Download strange_odetest_result_june_6_2024.mw

Update

Until this bug is fixed, I added the following to my code which checks for odetest result. it looks for 0^anything and changes it to 0. 

ode:=diff(y(x), x)^n= 0;
sol:=dsolve(ode);
stat:=odetest(sol,ode);
if patmatch(stat,0^a::anything) then 0; else stat; fi

gives    0

I found this problem when using odetest to check mysolution for this ode and was not getting 0 as expected,.

 

simplification challenge. Exponentials in express...

Asked by: nm 11353
simplify simplification
June 06 2024
1  2

These two expressions are the same

e1:=-sqrt(-(exp(-2 + 2*x) - 2)*exp(-2 + 2*x))/(exp(-2 + 2*x) - 2);
e2:=1/sqrt(2*exp(-2*x)*exp(2) - 1);

Is there an automated way to simplify e1 to e2? Below are my attempts. The closest I got is 

simplify(e1) assuming real;

But that still does not give same as e2. I can do it by "hand" as shown. But I like to find automated way since this is done in code without looking at expression. So I can't use the "hand" method there.

We can assume everything in real domain.


 

15244

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

e1:=-sqrt(-(exp(-2 + 2*x) - 2)*exp(-2 + 2*x))/(exp(-2 + 2*x) - 2);
e2:=1/sqrt(2*exp(-2*x)*exp(2) - 1);
plot([e1,e2],x=-3..3)

-(-(exp(-2+2*x)-2)*exp(-2+2*x))^(1/2)/(exp(-2+2*x)-2)

1/(2*exp(-2*x)*exp(2)-1)^(1/2)

> 

simplify(e1,size);
simplify(e1,symbolic);
simplify(e1) assuming real; #closest but still no cigar
 

-(-(exp(-2+2*x)-2)*exp(-2+2*x))^(1/2)/(exp(-2+2*x)-2)

-I*exp(-1+x)/(exp(-2+2*x)-2)^(1/2)

exp(-1+x)/(-exp(-2+2*x)+2)^(1/2)

> 

#can do it "by hand" by dividing upstairs and downstrais by numerator
A:=exp(-1 + x);
B:=-exp(-2 + 2*x) + 2;
e3:=1/sqrt( simplify(expand(B/A^2)))

exp(-1+x)

-exp(-2+2*x)+2

1/(-1+2*exp(2-2*x))^(1/2)

> 

#verify
plot([e3,e2],x=-3..3)

 

 


Download simplification_june_6_2024.mw

Selecl Remove from a set...

Asked by: Ronan 1341
type selectremove
June 05 2024
1  5

How do I get the susset that contains unknowns on the rhs of the elements?

> 

restart
> 

 

> 

# I need this subset {a=1/sqrt(2+A), b=6*sqrt(4+N),  d=5*H}
> 

 

> 

C:={a=1/sqrt(2+A),b=6*sqrt(4+N) ,c=sqrt(7),d=5*H,,e=-12,f=-96}

{a = 1/(2+A)^(1/2), b = 6*(4+N)^(1/2), c = 7^(1/2), d = 5*H, e = -12, f = -96}

 (1)
> 

selectremove(has,indets(rhs~(C)),C)

{}, {A, H, K, N, 1/(2+A)^(1/2), (4+N)^(1/2)}

 (2)
> 

selectremove(has,lhs~(C)=indets(rhs~(C)),C)

() = (), {a, b, c, d, e} = {H, K, N, (4+N)^(1/2)}

 (3)
 

 

Download 2024-06-05_Q_Select_Remove_indet_elements.mw

why dsolve gives this extra solution?...

Asked by: nm 11353
ode dsolve differential-equations
June 05 2024
1  5

We see that this ode (x + y(x))*(1+diff(y(x),x)) = 0  has 2 solutions, One when (x + y(x))=0 and one when (1+diff(y(x),x))=0. Maple gives 3 solutions. They are correct but why?

Also when changing (1+diff(y(x),x)) to (a+diff(y(x),x)) now it gives only two solution.

Why does this happen? Should it not just return 2 solutions in both cases? and more strange one

(x + y(x))^2 *(1+diff(y(x), x))=0; now it gives 4 solutions. But this is no different. We also have 2 solutions. One when (x + y(x))=0 and one when (1+diff(y(x), x))=0. This time the extra two solutions are complex. 

17168

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1754 and is the same as the version installed in this computer, created 2024, June 3, 20:39 hours Pacific Time.`

> 

ode:=(x + y(x))*(a+diff(y(x),x)) = 0;
dsolve(ode);
map(X->odetest(X,ode),[%])

(x+y(x))*(a+diff(y(x), x)) = 0

y(x) = -x, y(x) = -a*x+c__1

[0, 0]

> 

ode:=(x + y(x))*(1+diff(y(x),x)) = 0;
dsolve(ode);
map(X->odetest(X,ode),[%])

(x+y(x))*(1+diff(y(x), x)) = 0

y(x) = -x, y(x) = -x-c__1, y(x) = -x+c__1

[0, 0, 0]

> 

ode:= (x + y(x))^2 *(1+diff(y(x), x))=0;
dsolve(ode);
map(X->odetest(X,ode),[%])
> 

 

(x+y(x))^2*(1+diff(y(x), x)) = 0

y(x) = -x, y(x) = -x+c__1, y(x) = -(1/2)*c__1-((1/2)*I)*3^(1/2)*c__1-x, y(x) = -(1/2)*c__1+((1/2)*I)*3^(1/2)*c__1-x

[0, 0, 0, 0]

 

 

Download why_extra_solution_from_dsolve_june_5_2024.mw

why maple dsolve sometimes does not solve ode as o...

Asked by: nm 11353
ode dsolve differential-equations
June 05 2024
0  1

Any idea why this sometimes happens? odeadvisor says ode is quadrature but when asking it to solve it using quadrature sometimes it works and sometimes not.

Am I doing something wrong?

22020

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1754 and is the same as the version installed in this computer, created 2024, June 3, 20:39 hours Pacific Time.`

> 

restart;

18368

Example 1 that does not work

 
> 

ode:=diff(y(x),x)=-1;
DEtools:-odeadvisor(ode);

diff(y(x), x) = -1

[_quadrature]

> 

sol:=dsolve(ode,y(x),['quadrature']);

"sol := "

Example 2 that works

 
> 

ode:=diff(y(x),x)=x;
DEtools:-odeadvisor(ode);

diff(y(x), x) = x

[_quadrature]

> 

sol:=dsolve(ode,y(x),['quadrature']);

y(x) = (1/2)*x^2+c__1

 

 

Download sometimes_dsolve_works_on_quadrature_june_5_2024.mw

ODESteps gives Error, (in evalf/int) invalid argum...

Asked by: nm 11353
ode step-by-step differential-equations
June 03 2024
1  5

Any one could find why Maple 2024 gives Error, (in evalf/int) invalid arguments on this ode? Why is it even calling evalf in first place as this is all symbolic.

Also reported to Maplesof just in case.

25504

> 

restart;

25504

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1752 and is the same as the version installed in this computer, created 2024, May 31, 18:17 hours Pacific Time.`

> 

ode:=diff(y(x), x)^3 = (x - 2)^2;
ic:=y(2)=1;
Student:-ODEs:-ODESteps([ode,ic]);

(diff(y(x), x))^3 = (x-2)^2

y(2) = 1

Error, (in evalf/int) invalid arguments

> 

dsolve([ode,ic])

y(x) = 1+(1/5)*(3*x-6)*RootOf(_Z^3-x^2+4*x-4)

> 

DEtools:-odeadvisor(ode)

[_quadrature]

 

 

Download odetest_internal_error_evalf_int_june_3_2024.mw

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