First Order ODE/y' + y = 0

Theorem
The first order ODE:
 * $\dfrac {\d y} {\d x} + y = 0$

has the general solution:
 * $y = C e^{-x}$

where $C$ is an arbitrary constant.

Proof
This first order ODE is in the form:


 * $\dfrac {\d y} {\d x} + k y = 0$

where $k = 1$.

From First Order ODE: $\d y = k y \rd x$, this has the solution:


 * $y = C e^{-x}$