The general solution of the differential equation d y d x = 3 x+y x-y is (where C is a constant of integration.)

Step-by-step solution

d y d x = 3 x+y x-y aligned & v=x d v d x = 3+v 1-v [ let y=v x] & x d v d x = 3+v 1-v -v & x d v d x = 3+v^2 1-v & 1-v 3+v^2 d v= d x x & d v 3+v^2 - 1 2 2 v d v 3+v^2 = d x x & 1 3 ⁻¹ v 3 - 1 2 (3+v^2 )= x+C aligned aligned & 1 3 ⁻¹ y x 3 - 1 2 ( 3 x^2+y^2 x^2 )= x+C & 1 3 ⁻¹ y x 3 - ( y^2+3 x^2 x^2 )^ 1 2 = x+C aligned