How does one obtain all solutions from dsolve? I see an option called Allsolutions, but this seems to only apply to solve and other functions. It does not work with dsolve.
For example, maple gives one solution for the following first order non-linear ODE. But the ODE has another solution y(x)=0 as well. How does one tell Maple to return all solutions? I am interested in this when using the 'implicit' option mainly. Here is an example
But when I tried y(x)=0, it turned out to also be a solution
But dsolve did not return this solution on its own along with the first one. But on another example, Maple did well, and returned all solutions. Here is the other example
In the above, Maple returned the two solutions.
Is there a correct way to tell Maple dsolve to return all solutions all the time? Why did it return both solution in the above example, but not in the first example?
I am maple newbie. Thank you.