What is the solution for y^{''}+3y^'+2y=e^x-e^{-x} ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y = 7 sec (2 x)

y^{^{''}} - 2 y^{^{'}} + 5 y = 2

y^{^{''}} + 36 y = sec (6 x)

y^{^{''}} + 16 y = t^{2} + 1, y (0) = 0, y^{^{'}} (0) = 1

y^{^{'''}} - 12 y^{^{''}} + 48 y^{^{'}} - 64 y = 9 e^{4 x}

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