Solve the following differential equation: x^2(dy/dx) = x^2 + xy + y^2

Question

Solve the following differential equation:

x²\(\cfrac{dy}{dx}\) = x² + xy + y²

Answer 1

x²\(\cfrac{dy}{dx}\) = x² + xy + y²

\(\therefore\) \(\cfrac{dy}{dx} = \) \(\cfrac{x^2+xy+y^2}{x^2}....(1)\)

Put y = vx

Integrating, we get

This is the general solution.