What is the solution for (D^2-D)y=e^xsin(x) ?

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

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(D^2-D)y=e^xsin(x)

(D^{2} - D) y = e^{x} sin (x)

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

Solution steps

(D^{2} - D) y = e^{x} sin (x)

Solve linear ODE:

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

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

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