Question

The differential equation of $y = e^x (a \cos x + b \sin x)$ is

• A. $\frac{d^{2}y}{dx^{2}}-2\frac{dy}{dx}-y=0$
• B. $\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+2y=0$
• C. $\frac{d^{2}y}{dx^{2}}-2\frac{dy}{dx}+y=0$
• D. $\frac{d^{2}y}{dx^{2}}-2\frac{dy}{dx}+2y=0$

Hint:

Calculus Tip: When forming a differential equation, the order of the resulting highest derivative will always equal the number of arbitrary independent constants in the original equation (here, $a$ and $b$ mean we differentiate twice).
• Always look to substitute $y$ or $y'$ back into the differentiated equations to quickly eliminate constants.

Answer 1

The Correct Option is D