$y=x^3+c y$

$x=y^3+c y$

$y(1-x y)=c x$

$x(1-x y)=c y$

$3(y-1)^2-2(x+2)(y-1)-(x+2)^2=C$

$x^2-3 y^2-4 x y-2 x-10 y=C$

$3(y+1)^2+2(x-2)(y+1)-(x-2)^2=C$

$x^2+3 y^2+4 x y+2 x+10 y=C$

$\frac{d^2 y}{d x^2}-(x-1) \frac{d y}{d x}=0$

$(x-1) \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$

$\frac{d^2 y}{d x^2}+(x-1) \frac{d y}{d x}-y=0$

$(x-1) \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$

$y=x e^x+c$

$y=x e^x+c e^{-x}$

$y=\frac{e^x+c}{x}$

$y=\frac{e^{-x}+c x}{x}$