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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{x + 1}{x}

\frac{d y}{d x} = \frac{1}{x y + x + y + 1}

\frac{d}{d x} (csc (7 x))

\int (e^{2 x} - 5 x)^{2} d x

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