Correct Answer  Option 2 :
\(\rm \frac{d^2y}{dx^2}y=0\)
Concept:

Differential Equation: A differential equation is an equation that relates one or more functions and their derivatives.
 e.g. \(\rm \frac{dy}{dx}\) + x = 2y + 3, etc.
 \(\rm \dfrac{d}{dx}e^{f(x)}=\dfrac{d}{dx}f(x)e^{f(x)}\)
Calculation:
y = aex + bex
⇒ \(\rm \frac{dy}{dx}=\frac{d}{dx}ae^x +\frac{d}{dx}be^{x}\)
⇒ \(\rm \frac{dy}{dx}\) = aex  bex
⇒ \(\rm \frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}(ae^x be^{x})\)
⇒ \(\rm \frac{d^2y}{dx^2}\) = aex + bex = y
∴ The general solution of y = aex + bex is \(\rm \frac{d^2y}{dx^2}\)  y = 0.