If $y = 3e^{2x}+2e^{3x},$ then which one of the following is true ?

$\frac{d^2y}{dx^2}-5\frac{dy}{dx}+6y = 0 $

The correct answer is Option (2) → $\frac{d^2y}{dx^2}-5\frac{dy}{dx}+6y = 0 $

$y = 3e^{2x}+2e^{3x}$

$⇒\frac{dy}{dx}=6e^{2x}+6e^{2x}$

$⇒\frac{d^2y}{dx^2}=12e^{2x}+12e^{2x}$

Now,

$\frac{d^2y}{dx^2}-5\frac{dy}{dx}+6y=12e^{2x}+12e^{2x}-30e^{2x}-30e^{2x}+18e^{2x}+18e^{2x}$

$=0$