The DE requires a quite particular approach. We have...

(1)

Now if we differentiate both terms of (1) we obtain...

(2)

... and the (2) is satisfied for...

(3)

...or...

(4)

Thesystem of (1) and (3) has solution...

(5)

... and that is the general solution of (1). The system of (1) and (4) has as solution a 'particular solution' of (1) and it requires an easy procedure...

Kind regards