What is the solution for y^{''}+36y=288sin(6x)+96cos(6x) ?

The solution for y^{''}+36y=288sin(6x)+96cos(6x) is y=c_{1}cos(6x)+c_{2}sin(6x)+8xsin(6x)-24xcos(6x)

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y^{''}+36y=288sin(6x)+96cos(6x)

y^{^{''}} + 36 y = 288 sin (6 x) + 96 cos (6 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x) + 8 x sin (6 x) - 24 x cos (6 x)

Solution steps

y^{''} (x) + 36 y = 288 sin (6 x) + 96 cos (6 x)

Solve linear ODE:

y = c_{1} cos (6 x) + c_{2} sin (6 x) + 8 x sin (6 x) - 24 x cos (6 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x) + 8 x sin (6 x) - 24 x cos (6 x)

y^{^{''}} - y^{^{'}} - 2 y = 1, + t y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 10 sin (x)

(D^{2} + 2 D + 2) y = x^{2} + x + 1

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

y^{^{''}} + y = 3 x^{2} + 4

What is the solution for y^{''}+36y=288sin(6x)+96cos(6x) ?
The solution for y^{''}+36y=288sin(6x)+96cos(6x) is y=c_{1}cos(6x)+c_{2}sin(6x)+8xsin(6x)-24xcos(6x)