Solve the following differential equations : x cos(y/x){ydx + xdy} = y sin(y/x){xdy - ydx}

Question

Solve the following differential equations :

x cos\((\frac{y}{x})\) {ydx + xdy} = y sin\((\frac{y}{x})\) {xdy - ydx}

Answer 1

It is a homogeneous equation

Put y = vx

Integrating Both sides we get,