What is the solution for y^{''}-y^'-6y=250te^{-2t} ?

The solution for y^{''}-y^'-6y=250te^{-2t} is y=c_{1}e^{3t}+c_{2}e^{-2t}-25t^2e^{-2t}-10e^{-2t}t

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y^{''}-y^'-6y=250te^{-2t}

y^{^{''}} - y^{^{'}} - 6 y = 250 t e^{- 2 t}

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - 25 t^{2} e^{- 2 t} - 10 e^{- 2 t} t

Solution steps

y^{''} (t) - y^{'} (t) - 6 y = 250 t e^{- 2 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - 25 t^{2} e^{- 2 t} - 10 e^{- 2 t} t

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - 25 t^{2} e^{- 2 t} - 10 e^{- 2 t} t

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2}

y^{^{''}} - 3 y^{^{'}} + 2 y = x^{2} + x

y^{^{''}} - 8 y^{^{'}} + 16 y = \frac{e ^{4 x}}{x}

(2 D^{2} - 3 D + 1) y = csc (2 π x)

d, d (x) = \frac{x ^{2} + 13 x + 42}{x ^{2} - 3 x - 28}

What is the solution for y^{''}-y^'-6y=250te^{-2t} ?
The solution for y^{''}-y^'-6y=250te^{-2t} is y=c_{1}e^{3t}+c_{2}e^{-2t}-25t^2e^{-2t}-10e^{-2t}t