What is the solution for (d^2+5d+6)*y=e^x+e^{-x} ?

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

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(d^2+5d+6)*y=e^x+e^{-x}

(d^{2} + 5 d + 6) \cdot y = e^{x} + e^{- x}

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

Solution steps

(d^{2} + 5 d + 6) y = e^{x} + e^{- x}

Solve linear ODE:

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

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

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