What is the solution for y^{''}+4y^'+4y=375*t ?

The solution for y^{''}+4y^'+4y=375*t is y=c_{1}e^{-2t}+c_{2}te^{-2t}+(375t)/4-375/4

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y^{''}+4y^'+4y=375*t

y^{^{''}} + 4 y^{^{'}} + 4 y = 375 \cdot t

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{375 t}{4} - \frac{375}{4}

Solution steps

y^{''} (t) + 4 y^{'} (t) + 4 y = 375 \cdot t

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{375 t}{4} - \frac{375}{4}

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{375 t}{4} - \frac{375}{4}

y^{^{''}} - 2 y^{^{'}} - 15 y = 4 e^{t}

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = u

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 x^{2} - 2 x + 1 + sin (x)

y^{^{''}} - y + 3 = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 x + 6

What is the solution for y^{''}+4y^'+4y=375*t ?
The solution for y^{''}+4y^'+4y=375*t is y=c_{1}e^{-2t}+c_{2}te^{-2t}+(375t)/4-375/4