Find the solution of this differential equation dy/dx= 4x +xy^2 / y - x^2y

Question

The answer must ( 4+y^2) (1-x^2)= c

Answer 1

SEPARATION OF VARIABLES

Rewrite the DE:

dy/dx=(x/(1-x²))(4+y²)/y,

ydy/(4+y²)=xdx(1-x²).

Integrate both sides:

½ln(4+y²)=-½ln|1-x²|+K, where K is a constant,

½ln|(4+y²)(1-x²)|=K,

ln|(4+y²)(1-x²)|=2K,

(4+y²)(1-x²)=e²ᴷ=c, a different constant.