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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} = t

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

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

(D^{2} - 3 D) y = - 18 x

y^{^{''}} - 7 y^{^{'}} + 12 y = e^{3 x} + e^{4 x}

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