Question

Following are the parts of general solution of \[ \frac{d^2y}{dx^2}+2\frac{dy}{dx}+y=x\cos x: \]
A. \((C_1+C_2x)e^{-x\),
B. \((C_1+C_2x)e^x\),
C. \(\frac{x\sin x}{2}+\frac{\cos x}{2}+\frac{\sin x}{2}\),
D. \(\frac{x\sin x}{2}+\frac{\cos x}{2}-\frac{\sin x}{2}\).}

• A. A, C
• B. A, D
• C. B, C
• D. B, D

Hint:

For linear differential equations, first find the complementary function from the auxiliary equation and then add the particular integral.

Answer 1

The Correct Option is B