What is the solution for (D^2+3D+2)y=sin(e^x) ?

The solution for (D^2+3D+2)y=sin(e^x) is y=c_{1}e^{-x}+c_{2}e^{-2x}-e^{-2x}sin(e^x)

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(D^2+3D+2)y=sin(e^x)

(D^{2} + 3 D + 2) y = sin (e^{x})

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

Solution steps

(D^{2} + 3 D + 2) y = sin (e^{x})

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

What is the solution for (D^2+3D+2)y=sin(e^x) ?
The solution for (D^2+3D+2)y=sin(e^x) is y=c_{1}e^{-x}+c_{2}e^{-2x}-e^{-2x}sin(e^x)