What is the general solution of $\frac{dy}{dx} + y = \cos x$?

Explanation

1. 01

   The factor is $e^{x}$, so $ye^{x} = \int e^{x}\cos x\,dx$.

2. 02

   By parts twice, $\int e^{x}\cos x\,dx = \frac{e^{x}(\sin x + \cos x)}{2} + C$.

3. 03

   Divide by $e^{x}$: $y = \frac{\sin x + \cos x}{2} + Ce^{-x}$.