dx/dy=2x/y+3/y？ (*)

First, find the general solution of the corresponding homogeneous equation dx/dy = 2x/y.

dx/x=2dy/y

ln|x|=2ln|y|+ln|C|

That is x=Cy?

Set x=C(y)y by constant variation method?

Substitute it into the original equation (*)

C'(y)=3/y^4

C(y)=- 1/y^3 +C

Therefore, the general solution of the original equation is

x=(- 1/y^3 +C)y？

That is x=Cy? - 1/y

choose one