y=2 x+3 x satisfies which of the following differential equations?...

$$\begin{aligned} \frac{d y}{d x} & =-2 \cdot \sin x+3 \cos x \\ \text{\text{ and } } \frac{d^2 y}{d x^2} & =-2 \cdot \cos x-3 \sin x\end{aligned}$$$$\begin{aligned} & =-(2 \cos x+3 \sin x) \\ & =-y \end{aligned}$$$Hence,$\frac{d^2 y}{d x^2}+y=0$satisfied Again,$\left(\frac{d y}{d x}\right)^2+\frac{d y}{d x}=0\frac{d y}{d x}\left(\frac{d y}{d x}+1\right)=0$either$\frac{d y}{d x}=0$or$\frac{d y}{d x}=-1$i.e.,$-2 \sin x+3 \cos x=0$or,$-2 \sin x+3 \cos x=-1$or,$2 \sin x=3 \cos x\tan x=\frac{3}{2}$This is satisfied for$x=\tan ^{-1} \left(\frac{3}{2}\right)$