1.
Differential equations are solved by reducing them to the exact differential of an expression in xx and yy i.e., they are reduced to the form d(f(x,y))=0d(f(x,y)) = 0.

e.g.: xdx+ydyx2+y2=ydxxdyx2\frac{x\,dx + y\,dy}{\sqrt{x^2 + y^2}} = \frac{y\,dx - x\,dy}{x^2}
122xdx+2ydyx2+y2=xdyydxx2d(x2+y2)=d(yx)\Rightarrow \frac{1}{2}\frac{2x\,dx + 2y\,dy}{\sqrt{x^2 + y^2}} = -\frac{x\,dy - y\,dx}{x^2} \Rightarrow d\left(\sqrt{x^2 + y^2}\right) = -d\left(\frac{y}{x}\right)
d(x2+y2+yx)=0\Rightarrow d\left(\sqrt{x^2 + y^2} + \frac{y}{x}\right) = 0

\therefore solution is x2+y2+yx=c\sqrt{x^2 + y^2} + \frac{y}{x} = c

Use the above method to answer the following question:

The general solution of (2x3xy2)dx+(2y3x2y)dy=0(2x^3 - xy^2)\,dx + (2y^3 - x^2y)\,dy = 0 is