What is the solution for x^{''}-x^'-12x=e^{4t} ?

The solution for x^{''}-x^'-12x=e^{4t} is x=c_{1}e^{4t}+c_{2}e^{-3t}+(e^{4t}t)/7

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x^{''}-x^'-12x=e^{4t}

x^{^{''}} - x^{^{'}} - 12 x = e^{4 t}

x = c_{1} e^{4 t} + c_{2} e^{- 3 t} + \frac{e ^{4 t} t}{7}

Solution steps

x^{''} (t) - x^{'} (t) - 12 x = e^{4 t}

Solve linear ODE:

x = c_{1} e^{4 t} + c_{2} e^{- 3 t} + \frac{e ^{4 t} t}{7}

x = c_{1} e^{4 t} + c_{2} e^{- 3 t} + \frac{e ^{4 t} t}{7}

y^{^{''}} - 60 y^{^{'}} - 900 y = 5 e^{10 x}

y^{^{''}} - 16 y = x e^{x}

y^{^{''}} - 2 y^{^{'}} - 8 y = e^{- 2 x} + 2 x^{2}

\frac{d ^{2} y}{d x ^{2}} + c^{2} y = sec^{2} (c x)

y^{^{''}} - 3 y^{^{'}} + 5 y = 4 x^{3} - 2 x

What is the solution for x^{''}-x^'-12x=e^{4t} ?
The solution for x^{''}-x^'-12x=e^{4t} is x=c_{1}e^{4t}+c_{2}e^{-3t}+(e^{4t}t)/7