If $y = 3e^{2x} + 2e^{3x}$, then $\frac{d^2y}{dx^2}+6y$ is equal to

$5\frac{dy}{dx}$

The correct answer is Option (2) → $5\frac{dy}{dx}$

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

$\frac{dy}{dx}=6e^{2x}+6e^{3x}$

$\frac{d^2y}{dx^2}=12e^{2x}+18e^{3x}$

$\frac{d^2y}{dx^2}+6y$

$=(12e^{2x}+18e^{3x})+6(3e^{2x}+2e^{3x})$

$=12e^{2x}+18e^{3x}+18e^{2x}+12e^{3x}$

$=30e^{2x}+30e^{3x}$

$=5(6e^{2x}+6e^{3x})$

$=5\frac{dy}{dx}$

The value of $\frac{d^2y}{dx^2}+6y$ is $5\frac{dy}{dx}$.