What is the solution for y^{''}-9y=4e^{-5t} ?

The solution for y^{''}-9y=4e^{-5t} is y=c_{1}e^{3t}+c_{2}e^{-3t}+1/4 e^{-5t}

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y^{''}-9y=4e^{-5t}

y^{^{''}} - 9 y = 4 e^{- 5 t}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + \frac{1}{4} e^{- 5 t}

Solution steps

y^{''} (t) - 9 y = 4 e^{- 5 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + \frac{1}{4} e^{- 5 t}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + \frac{1}{4} e^{- 5 t}

y^{^{''}} + 4 y = 3 cos (a t)

y^{^{'''}} + 9 y^{^{''}} + 27 y^{^{'}} + 27 y = 7 e^{- 3 x}

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 2 x^{2} - x + 1

y^{^{''}} - 3 y - 5 = e^{2} - 3 cos (3 x)

y^{^{''}} + 36 y = 24 sin (6 x)

What is the solution for y^{''}-9y=4e^{-5t} ?
The solution for y^{''}-9y=4e^{-5t} is y=c_{1}e^{3t}+c_{2}e^{-3t}+1/4 e^{-5t}