What is the solution for y^{''}+11y^'+18y=5sin(3x) ?

The solution for y^{''}+11y^'+18y=5sin(3x) is y=c_{1}e^{-2x}+c_{2}e^{-9x}+1/26 sin(3x)-11/78 cos(3x)

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y^{''}+11y^'+18y=5sin(3x)

y^{^{''}} + 11 y^{^{'}} + 18 y = 5 sin (3 x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 9 x} + \frac{1}{26} sin (3 x) - \frac{11}{78} cos (3 x)

Solution steps

y^{''} (x) + 11 y^{'} (x) + 18 y = 5 sin (3 x)

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 9 x} + \frac{1}{26} sin (3 x) - \frac{11}{78} cos (3 x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 9 x} + \frac{1}{26} sin (3 x) - \frac{11}{78} cos (3 x)

y^{^{''}} - 9 y^{^{'}} = 81 x^{2} + 7

y^{^{''}} + y = sec^{3} (x), y (0) = 1

- y^{^{''}} + 10 y^{^{'}} + 25 y = 30 x + 3

y^{^{''}} + 4 y = 5 sec (2 x)

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

What is the solution for y^{''}+11y^'+18y=5sin(3x) ?
The solution for y^{''}+11y^'+18y=5sin(3x) is y=c_{1}e^{-2x}+c_{2}e^{-9x}+1/26 sin(3x)-11/78 cos(3x)