What is the solution for y^{''}+y=6sin(2x) ?

The solution for y^{''}+y=6sin(2x) is y=c_{1}cos(x)+c_{2}sin(x)-2sin(2x)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

(D^{2} - 3 D + 2) y = cos (3 x)

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

y^{^{'''}} + y^{^{''}} = 6

y^{^{''}} + 3 y^{^{'}} - 4 y = 1, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 cos^{2} (t)

What is the solution for y^{''}+y=6sin(2x) ?
The solution for y^{''}+y=6sin(2x) is y=c_{1}cos(x)+c_{2}sin(x)-2sin(2x)