2024 IGCSE Additional Mathematics May/June 0606/21 Q7

It is given that \(y=mx^2+\dfrac x2+n\), where \(m\) and \(n\) are non-zero constants. It is also given that \(3\left(\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}\right)=\left(\dfrac{\mathrm{d}y}{\mathrm{d}x}\right)^2-y\) for all values of \(x\). Find the values of \(m\) and \(n\).[4]