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

The solution for (d^2y)/(dt^2)+2(dy)/(dt)-3y=e^t is y=c_{1}e^t+c_{2}e^{-3t}+(e^tt)/4

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(d^2y)/(dt^2)+2(dy)/(dt)-3y=e^t

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

y = c_{1} e^{t} + c_{2} e^{- 3 t} + \frac{e ^{t} t}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- 3 t} + \frac{e ^{t} t}{4}

y = c_{1} e^{t} + c_{2} e^{- 3 t} + \frac{e ^{t} t}{4}

y^{^{''}} + 8 y^{^{'}} + 17 y = 6 e^{- 40} cos (t)

y^{^{''}} + \frac{3}{2} y^{^{'}} = x + e^{2 x}

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d y}{d x} = - 5 x^{2}

y^{^{''}} + y^{^{'}} - 8 y = 9 e^{3 t}

y^{^{''}} + 4 y = 3 e^{3 t}

What is the solution for (d^2y)/(dt^2)+2(dy)/(dt)-3y=e^t ?
The solution for (d^2y)/(dt^2)+2(dy)/(dt)-3y=e^t is y=c_{1}e^t+c_{2}e^{-3t}+(e^tt)/4