The general solution of (y^2-x^3),dx-xy,dy=0, x0, is (C constant):

Question

The general solution of $(y^2-x^3)\,dx-xy\,dy=0$, $x
e0$, is (C constant):

Accepted Answer

$$y^2\,dx-xy\,dy = x^3\,dx \implies -y\,d(y/x)=x\,dx\quad(\text{after dividing by }x^2).$$

Integrating: $-\dfrac12\dfrac{y^2}{x^2}=x+c_1 \implies y^2+2x^3+cx^2=0$.

Solutions · 1