$y=c_{1}e^{-2x}+c_{2}e^{-x}$ is a solution of the differential equation
Answer & explanation
Correct answer: option 1
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 $\frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=0$