verify that the given function (implicit or explicit) is a solution of the corresponding differential equation (iii) $y=x\sin 3x:\frac{{{d}^{2}}y}{d{{x}^{2}}}+9y-6\cos 3x=0$ (iv) ${{x}^{2}}=2{{y}^{2}}\log y:({{x}^{2}}+{{y}^{2}})\frac{dy}{dx}-xy=0$