What is the solution for y^{''}+5y^'+6y=-5-e^x ?

The solution for y^{''}+5y^'+6y=-5-e^x is y=c_{1}e^{-2x}+c_{2}e^{-3x}-5/6-1/12 e^x

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y^{''}+5y^'+6y=-5-e^x

y^{^{''}} + 5 y^{^{'}} + 6 y = - 5 - e^{x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} - \frac{5}{6} - \frac{1}{12} e^{x}

Solution steps

y^{''} (x) + 5 y^{'} (x) + 6 y = - 5 - e^{x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} - \frac{5}{6} - \frac{1}{12} e^{x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} - \frac{5}{6} - \frac{1}{12} e^{x}

y^{^{''}} + 3 y^{^{'}} + 9 y = 8 sin (6 t)

y^{^{''}} - y^{^{'}} + 0.25 y = 3 + e^{\frac{x}{2}}

y^{^{''}} + 2 y^{^{'}} - 3 y = 8 x e^{x}

y^{^{''}} + 2 y = 5 t^{2} - 3, y (0) = 0, y^{^{'}} (0) = - 6

10 y^{^{''}} + 1000 y = 140 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}+5y^'+6y=-5-e^x ?
The solution for y^{''}+5y^'+6y=-5-e^x is y=c_{1}e^{-2x}+c_{2}e^{-3x}-5/6-1/12 e^x