If $y = 3e^{2x}+2e^{3x}$, then $\frac{d^2y}{dx^2}-5\frac{dy}{dx}$ is equal to:
Answer & explanation
Correct answer: option 2
$y=3e^{2x}+2e^{3x}.$
$\frac{dy}{dx}=6e^{2x}+6e^{3x}.$
$\frac{d^2y}{dx^2}=12e^{2x}+18e^{3x}.$
$\frac{d^2y}{dx^2}-5\frac{dy}{dx}=(12e^{2x}+18e^{3x})-5(6e^{2x}+6e^{3x}).$
$=12e^{2x}+18e^{3x}-30e^{2x}-30e^{3x}.$
$=-18e^{2x}-12e^{3x}.$
$\frac{d^2y}{dx^2}-5\frac{dy}{dx}=-18e^{2x}-12e^{3x}=-6y.$