What is the solution for x^{''}+16x=cos(4t) ?

The solution for x^{''}+16x=cos(4t) is x=c_{1}cos(4t)+c_{2}sin(4t)+(tsin(4t))/8

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x^{''}+16x=cos(4t)

x^{^{''}} + 16 x = cos (4 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

Solution steps

x^{''} (t) + 16 x = cos (4 t)

Solve linear ODE:

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

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

y^{^{''}} + 4 y = - 12 sin (2 x), y (0) = 1.8, y^{^{'}} (0) = 5

y^{^{''}} - 11 y^{^{'}} + 24 y = 13 + 24 x

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

y^{^{''}} + y^{^{'}} - 2 y = - 260 sin (3 t)

What is the solution for x^{''}+16x=cos(4t) ?
The solution for x^{''}+16x=cos(4t) is x=c_{1}cos(4t)+c_{2}sin(4t)+(tsin(4t))/8