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Why Maple 2025.1 can't solve this fi...

nm 11413 Maple 2025
ode dsolve differential-equations
August 25 2025
2 0

I was surprised that Maple can't solve this first order ode which is exact ode.

I solved by hand and Maple says my solution is correct.

Any one can find why Maple failed to solve this and if older versions can solve it? Also tried implicit option, but that did not help.

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

restart;
> 

ode:=diff(y(x),x) = (2*sin(2*x)-tan(y(x)))/x/sec(y(x))^2;

diff(y(x), x) = (2*sin(2*x)-tan(y(x)))/(x*sec(y(x))^2)

> 

sol:=dsolve(ode);

> 

mysol:=cos(2*x)+x*tan(y(x))=c__1;

cos(2*x)+x*tan(y(x)) = c__1

> 

odetest(mysol,ode);

0

 

 

Download maple_solving_exact_ode_august_25_2025.mw

Should not dsolve give implicit solution...

nm 11413 Maple 2025
ode dsolve implicit
August 22 2025
0 4

THis is problem from textbook. Maple do not give solution. 

But when asked for implicit solution, it gives one.  Should it not have done this automatically?

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

ode:=y(x)*diff(y(x),x) = a;
ic:=y(0) = b;
sol:=dsolve([ode,ic]);

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

y(0) = b

> 

sol:=dsolve([ode,ic],'implicit')

-2*a*x+y(x)^2-b^2 = 0

 

 

Download why_no_solution_maple_2025_1.mw

We see now there are two solutions for y(x), since quadratic.

So why dsolve do not solve this and at least give implicit solution automatically? Should this be reported as defect?

why Maple simplifies 1+sin(x)^2 to 2-cos...

nm 11413 Maple 2025
simplify simplification trig
August 20 2025
1 1

Any idea why Maple simplifies 1+sin(x)^2 to 2-cos(x)^2?  Leaf count is larger also.

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

e1:=1+sin(x)^2;

1+sin(x)^2

> 

e2:=simplify(e1)

-cos(x)^2+2

> 

MmaTranslator:-Mma:-LeafCount(e1)

6

> 

MmaTranslator:-Mma:-LeafCount(e2)

8

 

 

Download strange_simplification_august_20_2025.mw

bug report: int() gives Error, (in tool...

nm 11413 Maple 2025
integration int indefinite-integration
August 20 2025
1 1

Attached worksheet

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1877 and is the same as the version installed in this computer, created 2025, July 11, 19:24 hours Pacific Time.`

> 

restart;
> 

integrand:=1/2/x^(9/2)*2^(1/2)*Pi^(1/2)/(1/x)^(1/2)*cos(1/x);

(1/2)*2^(1/2)*Pi^(1/2)*cos(1/x)/(x^(9/2)*(1/x)^(1/2))

> 

int(integrand,x)

Error, (in tools/eval_foo/do) too many levels of recursion

 

 

Download internal_error_on_int_august_20_2025_maple_2025_1.mw

Update

fyi, Here is yet another int() error Error, (in type/trig) too many levels of recursion in Maple 2025.1. (also reported to Maplesoft).

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1877 and is the same as the version installed in this computer, created 2025, July 11, 19:24 hours Pacific Time.`

> 

restart;
> 

integrand:=(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2);

(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)

> 

int(integrand,x)

Error, (in type/trig) too many levels of recursion

> 

int(integrand,x)

(1/6)*(-c*(-1+sin(f*x+e)))^(1/2)*((3/4)*B*sin(f*x+e)*tan(f*x+e)*cos(2*f*x+2*e)+A*sin(2*f*x+2*e)-(3/8)*tan(f*x+e)*(((4/5)*B*sin(f*x+e)+A)*sin(3*f*x+3*e)+(44/15)*B*sin(f*x+e)^2+(5*A-6*B)*sin(f*x+e)-(32/3)*A))*a*c^2*(a*(1+sin(f*x+e)))^(1/2)/f

> 

restart;
> 

integrand:=(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2);
int(integrand,x)

(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)

Error, (in type/trig) too many levels of recursion

 

 

Download another_int_error_too_many_levels_maple_2025_1.mw

is this a weakness in simplify?...

nm 11413 Maple 2025
simplify simplification trig
June 04 2025
0 2

Wondering what the experts here think of this. Should not simplify have worked on this automatically? By trial and error, found that combine command is what simplified it the best.

But I think simplify should also have done the same.  

Interested to hear what others think, and why simplify (even using trig option) did not do it.   

The issue is that this is done in code, without lookin at the screen and deciding what to do based on what the expression "looks like".

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

A:=(((sin(sqrt(3)/2)*sqrt(3) - 3*cos(sqrt(3)/2))*cos(sqrt(3)*x/2) - sin(sqrt(3)*x/2)*(sqrt(3)*cos(sqrt(3)/2) + 3*sin(sqrt(3)/2)))*exp(-1/2 + x/2))/3 ;

(1/3)*((sin((1/2)*3^(1/2))*3^(1/2)-3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)-sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

B:=- exp(-1/2 + x/2)*(sqrt(3)*sin(sqrt(3)*(x - 1)/2) + 3*cos(sqrt(3)*(x - 1)/2))/3;

-(1/3)*exp(-1/2+(1/2)*x)*(3^(1/2)*sin((1/2)*3^(1/2)*(x-1))+3*cos((1/2)*3^(1/2)*(x-1)))

> 

simplify(A-B); #show these are same

0

> 

simplify(A,trig)

-(1/3)*((-sin((1/2)*3^(1/2))*3^(1/2)+3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)+sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

simplify(A)

-(1/3)*((-sin((1/2)*3^(1/2))*3^(1/2)+3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)+sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

simplify(A,size)

-(1/3)*((-sin((1/2)*3^(1/2))*3^(1/2)+3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)+sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

simplify(normal(A))

-(1/3)*((-sin((1/2)*3^(1/2))*3^(1/2)+3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)+sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

combine(A); #finally

(-(1/3)*3^(1/2)*sin((1/2)*3^(1/2)*(x-1))-cos((1/2)*3^(1/2)*(x-1)))*exp(-1/2+(1/2)*x)

 

 

Download simplify_vs_combine_june_4_2025.mw

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