What is the solution for x^{''}+16x=14cos(3t) ?

The solution for x^{''}+16x=14cos(3t) is x=c_{1}cos(4t)+c_{2}sin(4t)+2cos(3t)

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x^{''}+16x=14cos(3t)

x^{^{''}} + 16 x = 14 cos (3 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) + 2 cos (3 t)

Solution steps

x^{''} (t) + 16 x = 14 cos (3 t)

Solve linear ODE:

x = c_{1} cos (4 t) + c_{2} sin (4 t) + 2 cos (3 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) + 2 cos (3 t)

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

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

(D^{2} - D - 2) y = 6 e^{\frac{- t}{2}}

y^{^{''}} + y^{^{'}} = 2 sin (t), y (0) = 0, y^{^{'}} (0) = - 4

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

What is the solution for x^{''}+16x=14cos(3t) ?
The solution for x^{''}+16x=14cos(3t) is x=c_{1}cos(4t)+c_{2}sin(4t)+2cos(3t)