2022 ASRJC J2 MYCT P1 Q7

Using the substitution \(y=u{{x}^{2}}\), show that the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{2y}{x}+\frac{{{x}^{2}}\left( 1-2x \right)}{2\left( 1+4{{x}^{2}} \right)}\) can be reduced to \(\frac{\mathrm{d}u}{\mathrm{d}x}=\frac{1-2x}{2\left( 1+4{{x}^{2}} \right)}\).

Hence solve the differential equation, leaving your answer in the form \(y=\mathrm{f}\left( x \right)\).[4]