What is the solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=sin(e^x) ?

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

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(d^2y)/(dx^2)+3(dy)/(dx)+2y=sin(e^x)

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = sin (e^{x})

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 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^2y)/(dx^2)+3(dy)/(dx)+2y=sin(e^x) ?
The solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=sin(e^x) is y=c_{1}e^{-x}+c_{2}e^{-2x}-e^{-2x}sin(e^x)