2022 CJC J2 MYE P1 Q3

Show that the substitution \(v=x+4y+3\) reduces the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x}={{\left( x+4y+3 \right)}^{2}}\) to \(\frac{\mathrm{d}v}{\mathrm{d}x}=1+4{{v}^{2}}\).[2]

Hence, find the general solution of the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x}={{\left( x+4y+3 \right)}^{2}}\), giving your answer in the form \(y=\mathrm{f}\left( x \right)\).[4]