Question

The general solution of the differential equation $\frac{d^{2}y}{d{x}^2}+8\frac{dy}{dx}+16y=0$ is

• (A) (a + bx)e^5x
• (B) (ax + b)e^–4x
• (C) (a + bx²)e^4x 
• (D) (a + bx⁴)e^4x 

Answer 1

The Correct Option is B

Explanation:
$$\begin{array}{l}\frac{d^{2}y}{d{x}^2}+8\frac{dy}{dx}+16y=0\\ \text{ auxilary equation }{m}^2+8m+16=0\Rightarrow m=-4\\ \text{ Solution }y=(ax+b)e^{-4x}\end{array}$$