What is the solution for y^{''}+9y=8cos(3x)+12sin(3x) ?

The solution for y^{''}+9y=8cos(3x)+12sin(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+(4xsin(3x))/3-2xcos(3x)

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y^{''}+9y=8cos(3x)+12sin(3x)

y^{^{''}} + 9 y = 8 cos (3 x) + 12 sin (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{4 x sin ( 3 x )}{3} - 2 x cos (3 x)

Solution steps

y^{''} (x) + 9 y = 8 cos (3 x) + 12 sin (3 x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{4 x sin ( 3 x )}{3} - 2 x cos (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{4 x sin ( 3 x )}{3} - 2 x cos (3 x)

2 y^{^{''}} + 27 y = e^{t} - e^{- t}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - y^{^{'}} + 2 y = 6 e^{\frac{1}{2}}

y^{^{''}} + 16 y = 2 csc^{2} (4 x)

y^{^{''}} + 5 y^{^{'}} + 6 y = sin (x) - cos (2 x)

y^{^{''}} - 10 y^{^{'}} + 25 = e^{5 x} ln (4 + x^{2})

What is the solution for y^{''}+9y=8cos(3x)+12sin(3x) ?
The solution for y^{''}+9y=8cos(3x)+12sin(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+(4xsin(3x))/3-2xcos(3x)