What is the solution for y^{''}-9y=sin(3x) ?

The solution for y^{''}-9y=sin(3x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-1/18 sin(3x)

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y^{''}-9y=sin(3x)

y^{^{''}} - 9 y = sin (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{18} sin (3 x)

Solution steps

y^{''} (x) - 9 y = sin (3 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{18} sin (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{18} sin (3 x)

y^{^{''}} + 4 y = x^{2} + sin (2 x)

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

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 x e^{3 x}

y^{^{''}} - 4 y^{^{'}} + 3 y = 1

y^{^{''}} + 9 y = 2 cos (3 x) + 2 sin (3 x)

What is the solution for y^{''}-9y=sin(3x) ?
The solution for y^{''}-9y=sin(3x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-1/18 sin(3x)