What is the solution for (d^2y)/(dx^2)-9y=sin(3x) ?

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

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(d^2y)/(dx^2)-9y=sin(3x)

\frac{d ^{2} y}{d x ^{2}} - 9 y = sin (3 x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 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^{^{''}} + 16 y = cos (4 t), y (0) = 6, y^{^{'}} (0) = 8

y^{^{''}} + 3 y^{^{'}} + 2 y = 1, + 4 x e^{- 3 x} y (0) = 0

x^{^{''}} + x = t sin (2 t)

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

y^{^{''}} + y - 1 = 0

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