What is the solution for y^{''}-9y=sin(x) ?

The solution for y^{''}-9y=sin(x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-1/10 sin(x)

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y^{''}-9y=sin(x)

y^{^{''}} - 9 y = sin (x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{10} sin (x)

Solution steps

y^{''} (x) - 9 y = sin (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{10} sin (x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{10} sin (x)

What is the solution for y^{''}-9y=sin(x) ?
The solution for y^{''}-9y=sin(x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-1/10 sin(x)