First Order ODE/dy = k y dx

Theorem
Let $k \in \R$ be a real number.

The first order ODE:
 * $\dfrac {\mathrm d y} {\mathrm d x} = k y$

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

Also represented as
This first order ODE can also be represented as:


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

from which the solution is:
 * $y = C e^{-k x}$

Also see

 * Decay Equation