What is the solution for x^{''}+16x=cos(2t) ?

The solution for x^{''}+16x=cos(2t) is x=c_{1}cos(4t)+c_{2}sin(4t)+1/12 cos(2t)

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x^{''}+16x=cos(2t)

x^{^{''}} + 16 x = cos (2 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{12} cos (2 t)

Solution steps

x^{''} (t) + 16 x = cos (2 t)

Solve linear ODE:

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{12} cos (2 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{12} cos (2 t)

What is the solution for x^{''}+16x=cos(2t) ?
The solution for x^{''}+16x=cos(2t) is x=c_{1}cos(4t)+c_{2}sin(4t)+1/12 cos(2t)