What is the solution for y^{''}+y^'-12y=e^{-3t} ?

The solution for y^{''}+y^'-12y=e^{-3t} is y=c_{1}e^{3t}+c_{2}e^{-4t}-1/6 e^{-3t}

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y^{''}+y^'-12y=e^{-3t}

y^{^{''}} + y^{^{'}} - 12 y = e^{- 3 t}

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{1}{6} e^{- 3 t}

Solution steps

y^{''} (t) + y^{'} (t) - 12 y = e^{- 3 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{1}{6} e^{- 3 t}

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{1}{6} e^{- 3 t}

y = x^{2} + 1, (3, 10)

\frac{\partial}{\partial y} (sin (x \cdot y^{2}))

\frac{d}{d x} (sec^{2} (m θ))

x \to 0 lim (x + \frac{2 x ^{2} + x}{x})

\frac{d}{d x} (\frac{x + 5}{2 x ^{2} e ^{x}})

What is the solution for y^{''}+y^'-12y=e^{-3t} ?
The solution for y^{''}+y^'-12y=e^{-3t} is y=c_{1}e^{3t}+c_{2}e^{-4t}-1/6 e^{-3t}