First Order ODE/y' + y = 0
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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:
- $y = C e^{-x}$
Sources
- 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $3$: The Differential Equation: $(3.11)$