2010 IJC P1 Q6

Show, by means of the substitution \(w={{x}^{2}}y\), that the differential equation

\(x\frac{\mathrm{d}y}{\mathrm{d}x}+2y+3xy=0\)

Can be reduced to the form \(\frac{\mathrm{d}w}{\mathrm{d}x}=-3w\).[2]

Hence find \(y\) in terms of \(x\), given that \(y=-\frac{1}{2}\) when \(x=2\).[4]