Find the general solution of the differential equation dydx - y = sinx

Given equation dydx - y = sinx represents a linear equation.
The integrating factor is e-x.
So the solution of the differential equation is ye-x = ∫e-xsinx dx + c, where c is a constant.
⇒ ye-x = -e-x/2(sinx + cosx) + c
⇒ y = -sinx + cosx / 2 + cex