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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 e^{- 4 t}, y (0) = 1

y^{^{''}} - y^{^{'}} = e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 8 y^{^{'}} + 16 = 0, y (0) = 1, y^{^{'}} (0) = 0

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 15 sin (x) - 35 cos (x)

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