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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (\frac{x y}{x y + 4})

\frac{3 s e ^{- 3 s}}{4 s ^{2} + 64}

\frac{d}{d x} (x^{\frac{4}{3}} - x^{\frac{1}{3}})

f (x) = (7 - x) (\frac{5}{x ^{2}} - 8)

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

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