Question

Solve the following differential equations.$(y-x{y}^2)dx-(x+x^{2}y)dy=0$

Answer 1

$ydx-x{y}^{2}dx-xdy-x^{2}ydy=0$

$ydx-xdy-xy(ydx-xdy)=0$

or, $(ydx-xdy)(1-xy)=0$

or, $ydx-xdy=0$

or, $xdy=ydx$

or, $\frac{dy}{y}=\frac{dx}{x}$

Integrating both sides,

$logy=logx+c$.