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

Question

The general solution of the differential equation $\frac{d^2 y}{d x^2}+8 \frac{d y}{d x}+16 y=0$ is, $(A+B x) e^{5 x}$, $(\mathrm{A}+\mathrm{Bx}) \mathrm{e}^{-4 x}$, $\left(\mathrm{A}+\mathrm{Bx}^2\right) \mathrm{e}^{4 \mathrm{x}}$, $\left(A+B x^4\right) \mathrm{e}^{4 \mathrm{x}}$

MARKS App · Accepted Answer

Hints: $\frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{dx}^2}+8 \frac{\mathrm{dy}}{\mathrm{dx}}+16 \mathrm{y}=0$ auxilary equation $\mathrm{m}^2+8 \mathrm{~m}+16=0 \Rightarrow \mathrm{m}=-4$ Solution $y=(a x+b) e^{-4 x}$

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