Solve the given differential equation y(u ^ 2 + 2)du - (u ^ 3 - u)dy = 0

Answer 1

We can eparate variables: dy/y = (u² + 2)/(u³ - u)du; ∫dy/y = ∫(- 2/u +3/2(u + 1) + 3/2(u-1))du

lny = - 2lnu + 3/2ln(u + 1) + 3/2ln(u - 1) + lnC; y =C(u² - 1)^3/2/u².

We decomposite fraction (u² + 2)/(u³ - u)