What is the solution for y^{''}+7y^'+12y=2e^t ?

The solution for y^{''}+7y^'+12y=2e^t is y=c_{1}e^{-3t}+c_{2}e^{-4t}+1/10 e^t

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y^{''}+7y^'+12y=2e^t

y^{^{''}} + 7 y^{^{'}} + 12 y = 2 e^{t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{10} e^{t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 12 y = 2 e^{t}

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{10} e^{t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{10} e^{t}

t^{2} y^{^{''}} - 2 t y^{^{'}} + 2 y = 4 t^{2}

\int (a + x)^{3} d x

8 e^{- 3 s}

\int_{1}^{2} \frac{- 7 ln ( x )}{x ^{2}} d x

\int \frac{- 7}{cos ( x ) - 1} d x

What is the solution for y^{''}+7y^'+12y=2e^t ?
The solution for y^{''}+7y^'+12y=2e^t is y=c_{1}e^{-3t}+c_{2}e^{-4t}+1/10 e^t