What is the solution for y^{''}-3y^'+2y=4t+12e^{-t} ?

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

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y^{''}-3y^'+2y=4t+12e^{-t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 t + 12 e^{- t}

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

Solution steps

y^{''} (t) - 3 y^{'} (t) + 2 y = 4 t + 12 e^{- t}

Solve linear ODE:

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

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

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