91Ó°ÊÓ

Solve the following equations. $$ x(y-3) \frac{\mathrm{d} y}{\mathrm{~d} x}=4 y $$

Obtain the general solution of the equation \(2 x y \frac{\mathrm{d} y}{\mathrm{~d} x}=x^{2}-y^{2}\).

Use the substitution \(y=\frac{\nu}{x}\), where \(v\) is a function of \(x\) only, to transform the equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{y}{x}=x y^{2}\) into a differential equation in \(v\) and \(x\). Hence find \(y\) in terms of \(x\).