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

The solution for (d^2y)/(dx^2)-y=sin(x)+e^{-5x} is y=c_{1}e^x+c_{2}e^{-x}-1/2 sin(x)+1/24 e^{-5x}

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(d^2y)/(dx^2)-y=sin(x)+e^{-5x}

\frac{d ^{2} y}{d x ^{2}} - y = sin (x) + e^{- 5 x}

y = c_{1} e^{x} + c_{2} e^{- x} - \frac{1}{2} sin (x) + \frac{1}{24} e^{- 5 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - y = sin (x) + e^{- 5 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - \frac{1}{2} sin (x) + \frac{1}{24} e^{- 5 x}

y = c_{1} e^{x} + c_{2} e^{- x} - \frac{1}{2} sin (x) + \frac{1}{24} e^{- 5 x}

What is the solution for (d^2y)/(dx^2)-y=sin(x)+e^{-5x} ?
The solution for (d^2y)/(dx^2)-y=sin(x)+e^{-5x} is y=c_{1}e^x+c_{2}e^{-x}-1/2 sin(x)+1/24 e^{-5x}