Question

 Solve the differential equation, 

xdx + (y - x³)dx = 0.

Answer 1

We have  x dy + (y - x³) dx = 0

It is in the form of \(\frac{dy}{dx}\) + Py = Q, where P = \(\frac1x\) and Q = x²

\(\therefore\) IF \(e^{\int\frac 1x dx}=e^{log\,x}\)  = x

Hence, solution is y. x = ∫ x. x² dx + C

x y = \(\frac{x^4}4\) + C

⇒ y = \(\frac{x^3}4+\frac Cx\)