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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} + 2 y^{^{'}} + 2 y = 2 cos (2 t)

y^{^{''}} + 2 y^{^{'}} + 5 y = 2 sin (t)

y^{^{''}} + 4 y^{^{'}} = 3 x^{2} - 4

y^{^{''}} + 4 y^{^{'}} + 29 = 0

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