What is the solution for (D^2+D)(y)=sin(x) ?

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

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(D^2+D)(y)=sin(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

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