Based on what you said, this is why I always wondered why Maple sometimes changes the implicit solution to explicit one when adding initial conditions, which will cause odetest not to verify the solution then.
Using same ODE I gave, this is Maple's solution
ic:=y(0) = 1:
But this does not verify as is
It will verify, by getting the correct region (in this case when csgn() is -1), But this requires more work from the user to figure that out.
I wonder why Maple did not solve the constant of integration from the general solution (which is implicit, good) and kept the IVP solution implicit? This would cause odetest to verify it as is, with no more post-processing. For the above:
ic:=y(0) = 1:
sol:=dsolve(ode); #solve with no IC
Which is implicit. Now solve for _C1 but keep the solution implicit, something like
new_sol := eval(sol,the_constant)
Now the IVP solution remained implicit. The difference, is that now odetest verifies it as is
Any insight why dsolve does not do this instead of making the final IVP explicit which makes it harder to odetest it? I do know that one can force the IVP solution to be implicit using
But why not do this by default in such cases, since it generates solution that will odetest to 0 as is.Notice in this case, the general solution came out implicit on its own, without using the option 'implicit'. But not the IVP solution. There one had to force the solution to show as implicit.
This is what I do not understand why.
Maple 2022.1 on windows 10