The DE can be written as...

(1)

This type of equation has been solved in eighteenth century by the Italian mathematician Gabriele Manfredi with the substitution...

(2)

Applying (2) the (1) becomes...

(3)

In (3) ther variables are separated, so that we can integrate both terms and obtain the general solution of (1)...

(4)

Imposing the condition we obtain finally the solution in implicit form...

(5)

... that is represented here...

The Cauchy-Lipschitz condition in are satisfied and the (1) has only one solution for . However in the case that isn't and [easy to verify...] we have two different solution of (1)...

(6)

Kind regards