What is the solution for y^{''}+4y^'+4y=16t+13 ?

The solution for y^{''}+4y^'+4y=16t+13 is y=c_{1}e^{-2t}+c_{2}te^{-2t}+4t-3/4

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y^{''}+4y^'+4y=16t+13

y^{^{''}} + 4 y^{^{'}} + 4 y = 16 t + 13

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

Solution steps

y^{''} (t) + 4 y^{'} (t) + 4 y = 16 t + 13

Solve linear ODE:

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

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

What is the solution for y^{''}+4y^'+4y=16t+13 ?
The solution for y^{''}+4y^'+4y=16t+13 is y=c_{1}e^{-2t}+c_{2}te^{-2t}+4t-3/4