What is the solution for y^{''}-y=x+sin(x) ?

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

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y^{''}-y=x+sin(x)

y^{^{''}} - y = x + sin (x)

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

Solution steps

y^{''} (x) - y = x + sin (x)

Solve linear ODE:

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

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

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