What is the solution for y^{''}-y^'-6y=33sin(3x) ?

The solution for y^{''}-y^'-6y=33sin(3x) is y=c_{1}e^{3x}+c_{2}e^{-2x}-55/26 sin(3x)+11/26 cos(3x)

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y^{''}-y^'-6y=33sin(3x)

y^{^{''}} - y^{^{'}} - 6 y = 33 sin (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{55}{26} sin (3 x) + \frac{11}{26} cos (3 x)

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = 33 sin (3 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{55}{26} sin (3 x) + \frac{11}{26} cos (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{55}{26} sin (3 x) + \frac{11}{26} cos (3 x)

y^{^{'''}} + y^{^{''}} - 2 y = e^{3 x} (9 + 67 x + 17 x^{2})

x^{^{''}} - 3 x^{^{'}} - 28 x = sin (6 t)

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

y^{^{''}} - 8 y^{^{'}} + 80 y = - 2 sin (3 t)

0.25 y^{^{''}} + 0.25 y^{^{'}} + 16 y = 3 cos (2 t)

What is the solution for y^{''}-y^'-6y=33sin(3x) ?
The solution for y^{''}-y^'-6y=33sin(3x) is y=c_{1}e^{3x}+c_{2}e^{-2x}-55/26 sin(3x)+11/26 cos(3x)