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| $y=c_{1}e^{-2x}+c_{2}e^{-x}$ is a solution of the differential equation |
$\frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=0$ $\frac{d^2y}{dx^2}+2\frac{dy}{dx}+3y=0$ $\frac{d^2y}{dx^2}+2y=0$ $\frac{d^2y}{dx^2}+3\frac{dy}{dx}+5y=0$ |
| $\frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=0$ |
| Here $m_{1}=-2,m_{2}=-1$. So the auxilary equation is $(m+2)(m+1)=m^2+3m+2=0$. Hence the differential equation satisfies $\frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=0$ |
