What is the solution for y^{''}-9y=sin(2x) ?

The solution for y^{''}-9y=sin(2x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-1/13 sin(2x)

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y^{''}-9y=sin(2x)

y^{^{''}} - 9 y = sin (2 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{13} sin (2 x)

Solution steps

y^{''} (x) - 9 y = sin (2 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{13} sin (2 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{13} sin (2 x)

\frac{d ^{2} y}{d x ^{2}} + y = 32 x^{3}

y^{^{''}} - 0.16 y = 32 cosh (0.4 x)

y^{^{''}} + 9 y = e^{4 x} + 3 x^{2} - 5

y^{^{''}} + (- 4) y^{^{'}} + 4 y = \frac{2 e ^{2 x}}{x}

y^{^{''}} + 3 y^{^{'}} - 4 y = 6 e^{x}

What is the solution for y^{''}-9y=sin(2x) ?
The solution for y^{''}-9y=sin(2x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-1/13 sin(2x)