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)

(8 x^{^{''}} + 4 x^{^{'}} - 24) = 48 e^{2 t}

y^{^{''}} + 2 y^{^{'}} = 2 e^{- 2 t}

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

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{2} - 4

y^{^{''}} + 2 y^{^{'}} + y = x e^{- x} + 4

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)