(x+1) dy/dx= x (y^2+1)

Question

Solve by variable separation method.

Answer 1

 

Let us take integration on both sides

.

Comments

tan^-1 (y)= x - log (x+1) + c1

y = tan (x - log(x+1) + c1)

Answer 2

 

Let us take integration on both sides

Tan ^ -1 ( y ) = x - log ( x + 1 ) + c1

y =Tan [ x - log( x + 1) + c1].