What is the solution for (D^2+1)y=e^{ix} ?

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

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(D^2+1)y=e^{ix}

(D^{2} + 1) y = e^{i x}

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

Solution steps

(D^{2} + 1) y = e^{i x}

Solve linear ODE:

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

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

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