What is the solution for linear y^{''}+y=sin(x) ?

The solution for linear y^{''}+y=sin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(xcos(x))/2

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linear y^{''}+y=sin(x)

linear

y^{^{''}} + y = sin (x)

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

Solution steps

y^{''} (x) + y = sin (x)

Solve linear ODE:

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

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

What is the solution for linear y^{''}+y=sin(x) ?
The solution for linear y^{''}+y=sin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(xcos(x))/2