What is the solution for x^{''}-5x^'-6x=2e^{-3t} ?

The solution for x^{''}-5x^'-6x=2e^{-3t} is x=c_{1}e^{6t}+c_{2}e^{-t}+1/9 e^{-3t}

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x^{''}-5x^'-6x=2e^{-3t}

x^{^{''}} - 5 x^{^{'}} - 6 x = 2 e^{- 3 t}

x = c_{1} e^{6 t} + c_{2} e^{- t} + \frac{1}{9} e^{- 3 t}

Solution steps

x^{''} (t) - 5 x^{'} (t) - 6 x = 2 e^{- 3 t}

Solve linear ODE:

x = c_{1} e^{6 t} + c_{2} e^{- t} + \frac{1}{9} e^{- 3 t}

x = c_{1} e^{6 t} + c_{2} e^{- t} + \frac{1}{9} e^{- 3 t}

3 y^{^{''}} + 2 g^{2} y = 4.9 g cos (8 t)

x^{^{''}} + 2.8 x^{^{'}} + 4 x = 10, x (0) = 2, x^{^{'}} (0) = 3

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{- 6.5 e ^{- 2 t}}{t ^{2} + 1}

y^{^{''}} + 49 y = cos (7 t), y (0) = 8, y^{^{'}} (0) = 7

y^{^{''}} - 4 y^{^{'}} - 5 y = 7 e^{2} t

What is the solution for x^{''}-5x^'-6x=2e^{-3t} ?
The solution for x^{''}-5x^'-6x=2e^{-3t} is x=c_{1}e^{6t}+c_{2}e^{-t}+1/9 e^{-3t}