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

The solution for x^{''}+3x^'+2x=3(e^{(-3t)}) is x=c_{1}e^{-t}+c_{2}e^{-2t}+3/2 e^{-3t}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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