What is the solution for y^{''}+10y^'+25y=128e^{3t} ?

The solution for y^{''}+10y^'+25y=128e^{3t} is y=c_{1}e^{-5t}+c_{2}te^{-5t}+2e^{3t}

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y^{''}+10y^'+25y=128e^{3t}

y^{^{''}} + 10 y^{^{'}} + 25 y = 128 e^{3 t}

y = c_{1} e^{- 5 t} + c_{2} t e^{- 5 t} + 2 e^{3 t}

Solution steps

y^{''} (t) + 10 y^{'} (t) + 25 y = 128 e^{3 t}

Solve linear ODE:

y = c_{1} e^{- 5 t} + c_{2} t e^{- 5 t} + 2 e^{3 t}

y = c_{1} e^{- 5 t} + c_{2} t e^{- 5 t} + 2 e^{3 t}

d, d (x) = lo g_{10} (\frac{x + 4}{x - 1})

y^{^{''}} + 4 y^{^{'}} + y = 4

a y^{^{''}} + b y^{^{'}} = 1

y^{^{''}} - 2 y^{^{'}} + 2 y = sec (x) e^{x}

(D^{3} - D) y = x^{3}

What is the solution for y^{''}+10y^'+25y=128e^{3t} ?
The solution for y^{''}+10y^'+25y=128e^{3t} is y=c_{1}e^{-5t}+c_{2}te^{-5t}+2e^{3t}