What is the solution for y^{''}+5y^'+6y=2e^{-t} ?

The solution for y^{''}+5y^'+6y=2e^{-t} is y=c_{1}e^{-2t}+c_{2}e^{-3t}+e^{-t}

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y^{''}+5y^'+6y=2e^{-t}

y^{^{''}} + 5 y^{^{'}} + 6 y = 2 e^{- t}

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

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 2 e^{- t}

Solve linear ODE:

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

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

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

y^{^{''}} + 10 y^{^{'}} + 25 y = 100 sin (5 x)

(d^{2} + 1) y = sin (x)

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2 x} (cos (x) - 5 sin (x))

y^{^{''}} + 5 y^{^{'}} + 4 y = e^{- t}

What is the solution for y^{''}+5y^'+6y=2e^{-t} ?
The solution for y^{''}+5y^'+6y=2e^{-t} is y=c_{1}e^{-2t}+c_{2}e^{-3t}+e^{-t}