Question

Solve the differential equation dy/dx = x³y³ - xy

Answer 1

Here,

dy/dx + xy = x³y³

Therefore

1/y³(dy/dx) + x.1/y² = x³   (1)

Put 1/y² = z. Then

-2/y³(dy/dx) = dz/dx

Therefore, Eq. (1) becomes

- 1/2(dz/dx) + xz = x³

⇒ dz/dx - 2xz = -2x³

It is in the linear form. So, the integrating factor e^∫-2xdx = e^{-x^2}.

Multiplying by it,