2023 YIJC P1 Q7

It is given that \(\frac{\mathrm{d}y}{\mathrm{d}x}={{\left( 4x-y+2 \right)}^{2}}\). Using the substitution \(v=4x-y\), show that the differential equation can be transformed to \(\frac{\mathrm{d}v}{\mathrm{d}x}=\mathrm{f}\left( v \right)\), where the function \(\mathrm{f}\left( v \right)\) is to be found.[2]

Hence, given that \(y=-2\) when \(x=0\), solve the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x}={{\left( 4x-y+2 \right)}^{2}}\), to find \(y\) in terms of \(x\).[4]