Question

Solve: x dx + y dy = (x² + y²)y dy.

Answer 1

The given differential equation is

xdx + ydy = (x² + y²)y dy

(xdx + ydy)/(x² + y²) = ydy

(1/2)d(log(x² + y²)) = ydy

Integrating, we get

(1/2)(log(x² + y²)) = (y²/2) + (c/2)

log(x² + y²) = y² + c

which is the required solution.