I do not understand why Maple sometimes shows singular solution to Clairaut ODE and sometimes not.
Clairaut ODE has the form y(x) = x y'(x) + G(x, y')
In the following ODE when I ask Maple to dsolve it as is, it does give singular solution. Next, when solving explicity for y(x) first, which will generate 2 ODE's, each is Clairaut ODE, then ask Maple to dsolve each, now Maple no longer gives the singular solution. But when I solve each one of these ODE's, I see that there is the singular solution there. It must be there, since this is Clairaut ODE and it has singular solution.
When I do PDEtools:-casesplit on each of the two ODE's generated by solving for y(x) first, I see the singular solution there.
The question is, why Maple dsolve does not show the singular solution in the second case? And how to make it show it? Or did I do something wrong?