This second order (Euler type) ode has no solution for the given two initial conditions. but Maple gives solution with one unresolved constant of integration.
ode:=x^2*diff(y(x),x$2)-2*y(x)=0;
ic:=y(0)=4,D(y)(0)=-1;
sol_no_IC:=dsolve(ode)
The IC's are given at x=0 as a trick to see what Maple will do. We see that at x=0 there is division by zero. So no solution exist for these IC's. But see what happens
sol_with_IC:=dsolve([ode,ic])
It seems Maple simply threw away the part of the solution it could not handle due to the x=0 and just returned the rest.
odetest(sol_with_IC,[ode,ic])
The correct answer should have been the NULL solution (i.e. no solution).
What Am I missing here? Why does Maple do this? Should Maple have returned such a solution?
Maple 2024 on windows 10.
update:
Reported to Maplesoft support.
update:
Here is another example ode. This is first order ode. Maple gives a solution that does not satisfy the initial condition also. I wish I can understand how Maple comes up with these solutions since when I solve these by hand I see it is not possible to satisfy the IC, hence no solution exist.
Download another_strange_solution_ode_maple_2024.mw