What is the solution for y^{''}-6y^'+9y=4e^{-3t} ?

The solution for y^{''}-6y^'+9y=4e^{-3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+1/9 e^{-3t}

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y^{''}-6y^'+9y=4e^{-3t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 e^{- 3 t}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{1}{9} e^{- 3 t}

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = 4 e^{- 3 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{1}{9} e^{- 3 t}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{1}{9} e^{- 3 t}

y^{^{''}} + 5 y^{^{'}} + 6 y = sin (x)

y^{^{''}} - y^{^{'}} - 6 y = 70 cos (3 x)

y^{^{''}} + 4 y^{^{'}} + 13 y = - 2 sin (3 t)

2 y^{^{''}} + 3 y - 2 y = 6 x^{2} + 5 x - 8

\frac{3}{2} \frac{d ^{2} y}{d x ^{2}} + \frac{1}{80} \frac{d y}{d x} = g

What is the solution for y^{''}-6y^'+9y=4e^{-3t} ?
The solution for y^{''}-6y^'+9y=4e^{-3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+1/9 e^{-3t}