What is the solution for y^{''}+7y^'+12y=e^t ?

The solution for y^{''}+7y^'+12y=e^t is y=c_{1}e^{-3t}+c_{2}e^{-4t}+1/20 e^t

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y^{''}+7y^'+12y=e^t

y^{^{''}} + 7 y^{^{'}} + 12 y = e^{t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{20} e^{t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 12 y = e^{t}

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{20} e^{t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{20} e^{t}

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 e^{(- x)} cos (2 x)

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{8 e ^{- 3 x}}{x ^{2} + 1}

y^{^{'''}} + 2 y^{^{''}} = 32 e^{2 x} + 24 x

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{3 x}

What is the solution for y^{''}+7y^'+12y=e^t ?
The solution for y^{''}+7y^'+12y=e^t is y=c_{1}e^{-3t}+c_{2}e^{-4t}+1/20 e^t