Question

Solve by I.F method

-2xydy+(x²+y²)dx = 0

Answer 1

$-2xydy+(x^2+y^2)dx = 0$

$2yy'-y^2/x=x$

$v=y^2$

$v'-v/x=x$

integrating foctor:

$\mu=1/x$

$v'/x-v/x^2=1$

$v'/x+\frac{d}{dx}(1/x)v=1$

$\frac{d}{dx}(v/x)=1$

$v/x=x+c$

$y=\pm \sqrt{x(x+c)}$