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

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

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

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

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x sin (3 x)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x sin (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x sin (3 x)

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

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{2 x}}{( e ^{x} + 1 ) ^{2}}

y^{^{''}} + 2 y^{^{'}} + 2 y = 2 e^{- x} cos (x)

y^{^{''}} + y = 6 e^{- 7 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} - 5 y = t e^{t}, y (0) = 1, y^{^{'}} (0) = 0

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