nm

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These are questions asked by nm

What is the opinion here on the following. If given   A which is linear in x, but not simplified. now type(A,x) gives false.  But type(simplify(A),x) gives true.

Does this mean it is the user responsibility to simplify the expression first before calling type on it? 

Why does not type command do this internally to see if it is linear before deciding? What is the reason for this design choice?

interface(version);

`Standard Worksheet Interface, Maple 2025.2, Windows 10, November 11 2025 Build ID 1971053`

restart;

 

A:=(x+y+1)^2-(x+y-1)^2;

(x+y+1)^2-(x+y-1)^2

simplify(A);

4*x+4*y

type(A,linear(y))

false

type(simplify(A),linear(y))

true

type(A,linear(x))

false

type(simplify(A),linear(x))

true

 

 

Download why_simplify_is_needed_feb_9_2026.mw

Could someone suggest a way to help dsolve be able to obtain this solution to this complicated first order ode? In V 2025.2 it is not able to solve it as is

interface(version);

`Standard Worksheet Interface, Maple 2025.2, Windows 10, November 11 2025 Build ID 1971053`

ode:=-x*sqrt((1 - x)/(x + 1))*(x + 1)*arcsech(x)*diff(y(x), x)*exp(y(x)/arcsech(x) + exp(y(x)/arcsech(x))) - y(x)*exp(y(x)/arcsech(x) + exp(y(x)/arcsech(x))) + 2*x*sqrt((1 - x)/(x + 1))*(x + 1)*arcsech(x)^2 = 0;

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

sol:=dsolve(ode);

expected_sol:=y(x)=arcsech(x)*ln(ln(2*x+_C1));

y(x) = arcsech(x)*ln(ln(2*x+_C1))

odetest(expected_sol,ode) assuming x>0

0

 

 

Download ode_solution_feb_6_2026.mw

Noticed something strange.  When I type

restart;
F:=x-> (x^4+3*x^3-3*x^2-2*x-24)/(x^4-4*x^3-13*x^2+62*x-56);
u:=x->piecewise(x=-4,limit(F(x),x=-4),true,F(x));
u(-4);

Gives Error, (in F) numeric exception: division by zero which means it did not hit the first condition x=-4

But when I write this

restart;
F:=x-> (x^4+3*x^3-3*x^2-2*x-24)/(x^4-4*x^3-13*x^2+62*x-56);
A:=limit(F(x),x=-4);
u:=x->piecewise(x=-4,A,true,F(x));
u(-4)

Now it gives expected result 15/47

To avoid defining many variables, like A above, I'd like to just write the  limit inside.

Is there a way to make Maple accept the limit inside piecewise as written above? i.e. have it evaluate to 15/47?

Help says "The piecewise function evaluates its arguments on an as-needed basis."

Not sure what this means.

I tried adding eval, as in 

u:=x->piecewise(x=-4,eval(limit(F(x),x=-4)),true,F(x));

But this did nothing

Maple 2025.2

 

Should not the following two commands produce same solution?

f:=x->(x^2+3*x-4)*cos(x^2+3*x-5);
PDEtools:-Solve({f(x)=0,0<x,x<2},x);
solve({f(x)=0,0<x,x<2},x);

This is what the result looks like

Why Solve gives one solution and solve gives 2? Is this expected or a bug?

btw, the solution from solve is also not complete. There are 5 roots not 2.

Student:-Calculus1:-Roots(f(x),x=0..2);

 

Why when going to user pages and clicking to see the next page, Mapleprimes gives

https://mapleprimes.com/users/?page=2

This happens for each page after the first one which shows OK.

Do others see this also?

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