What is the solution for y^{''}-y^'-6y=e^t ?

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

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y^{''}-y^'-6y=e^t

y^{^{''}} - y^{^{'}} - 6 y = e^{t}

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

Solution steps

y^{''} (t) - y^{'} (t) - 6 y = e^{t}

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 25 y = 16 sin (x)

y^{^{''''}} - y = cos (x)

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

y^{^{''}} + 10 y^{^{'}} + 9 y = 6 cos (3 t + 1.5708) H (t)

\frac{d ^{2} y}{d x ^{2}} + 4 y = tan (2 x)

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