What is the solution for (d^2y)/(dt^2)-y=10e^t ?

The solution for (d^2y)/(dt^2)-y=10e^t is y=c_{1}e^t+c_{2}e^{-t}+5te^t

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(d^2y)/(dt^2)-y=10e^t

\frac{d ^{2} y}{d t ^{2}} - y = 10 e^{t}

y = c_{1} e^{t} + c_{2} e^{- t} + 5 t e^{t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - y = 10 e^{t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + 5 t e^{t}

y = c_{1} e^{t} + c_{2} e^{- t} + 5 t e^{t}

y^{^{''}} - 0 \cdot y^{^{'}} - 2 y = - 2 t + 4 t^{2}

y^{^{''}} - y = - 20 t + 2

y^{^{'''}} + 2 y^{^{''}} + y^{^{'}} = π e^{x} cos (x)

y^{^{''}} - y = 4 e^{- x}

y^{^{''}} + 8 y + 15 = - 18 e^{- 2 t}, y (0) = - 6, y^{^{'}} (0) = 10

What is the solution for (d^2y)/(dt^2)-y=10e^t ?
The solution for (d^2y)/(dt^2)-y=10e^t is y=c_{1}e^t+c_{2}e^{-t}+5te^t