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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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