What is the solution for (d^2x)/(dt^2)-3(dx)/(dt)+2x=e^t ?

The solution for (d^2x)/(dt^2)-3(dx)/(dt)+2x=e^t is x=c_{1}e^{2t}+c_{2}e^t-e^tt

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(d^2x)/(dt^2)-3(dx)/(dt)+2x=e^t

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 2 x = e^{t}

x = c_{1} e^{2 t} + c_{2} e^{t} - e^{t} t

Solution steps

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 2 x = e^{t}

Solve linear ODE:

x = c_{1} e^{2 t} + c_{2} e^{t} - e^{t} t

x = c_{1} e^{2 t} + c_{2} e^{t} - e^{t} t

What is the solution for (d^2x)/(dt^2)-3(dx)/(dt)+2x=e^t ?
The solution for (d^2x)/(dt^2)-3(dx)/(dt)+2x=e^t is x=c_{1}e^{2t}+c_{2}e^t-e^tt