What is the solution for y^{''}+y=sin(x)+sin(2x) ?

The solution for y^{''}+y=sin(x)+sin(2x) is y=c_{1}cos(x)+c_{2}sin(x)-(xcos(x))/2-1/3 sin(2x)

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y^{''}+y=sin(x)+sin(2x)

y^{^{''}} + y = sin (x) + sin (2 x)

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x cos ( x )}{2} - \frac{1}{3} sin (2 x)

Solution steps

y^{''} (x) + y = sin (x) + sin (2 x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x cos ( x )}{2} - \frac{1}{3} sin (2 x)

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x cos ( x )}{2} - \frac{1}{3} sin (2 x)

What is the solution for y^{''}+y=sin(x)+sin(2x) ?
The solution for y^{''}+y=sin(x)+sin(2x) is y=c_{1}cos(x)+c_{2}sin(x)-(xcos(x))/2-1/3 sin(2x)