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

The solution for y^{''}+9y=cos(9x) is y=c_{1}cos(3x)+c_{2}sin(3x)-1/72 cos(9x)

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

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

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{72} cos (9 x)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{72} cos (9 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{1}{72} cos (9 x)

y^{^{''}} - y^{^{'}} - 6 y = 32 cos (3 x)

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

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 3

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - 5 y^{^{'}} - 6 y = 10, y (0) = 2, y^{^{'}} (0) = 1

What is the solution for y^{''}+9y=cos(9x) ?
The solution for y^{''}+9y=cos(9x) is y=c_{1}cos(3x)+c_{2}sin(3x)-1/72 cos(9x)