Question: bug report: Student:-ODEs:-ODESteps gives wrong solutions sometimes using change of variable

Maple's Student:-ODEs:-ODESteps solves an ode by doing change of variable on the independent variable, but the resulting ode is wrong and final answer is wrong.

Here is one such example

restart;
ode:=diff(diff(y(x),x),x)*sin(x)^2 = 2*y(x);
Student:-ODEs:-ODESteps(ode):

But this result is wrong. First of all, we can not have both x and t  in the same ode. This is what dchange gives

ode:=diff(y(x),x$2)*sin(x)^2-2*y(x)=0;
tr:={PDEtools:-Solve(t=ln(x),x)};
simplify(PDEtools:-dchange(tr,ode,[t]))

It looks like Student:-ODEs:-ODESteps is trying to solve  sin(x)^2*y'' + 2 y=0 as EULER type ode.

But Euler type ode will look like  x^2*y'' +2 y=0  

It seems to have confused sin(x)^2 with x^2. This change of variable it used only works for EULER type ode with polynomial coefficient, not trig coefficients.

Maple 2024.2 on Windows 10