What is the solution for x^{''}-25x=3e^{2t} ?

The solution for x^{''}-25x=3e^{2t} is x=c_{1}e^{5t}+c_{2}e^{-5t}-1/7 e^{2t}

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x^{''}-25x=3e^{2t}

x^{^{''}} - 25 x = 3 e^{2 t}

x = c_{1} e^{5 t} + c_{2} e^{- 5 t} - \frac{1}{7} e^{2 t}

Solution steps

x^{''} (t) - 25 x = 3 e^{2 t}

Solve linear ODE:

x = c_{1} e^{5 t} + c_{2} e^{- 5 t} - \frac{1}{7} e^{2 t}

x = c_{1} e^{5 t} + c_{2} e^{- 5 t} - \frac{1}{7} e^{2 t}

(D^{3} + 3 D^{2} - 4) y = x e^{- 2 x}

y^{^{''}} - y = 1, y (0) = 0

y^{^{''}} + 4 y^{^{'}} + 6 y = 1, + e^{-} t y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = x sin (x)

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 14 t

What is the solution for x^{''}-25x=3e^{2t} ?
The solution for x^{''}-25x=3e^{2t} is x=c_{1}e^{5t}+c_{2}e^{-5t}-1/7 e^{2t}