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2025-09-30 13:19:25 -05:00
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docs/math/diffeq/1-intro.md
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@@ -14,7 +14,7 @@ This section is from [Paul's Online Math Notes](https://tutorial.math.lamar.edu/
**Definition**. A *linear* differential equation is any differential equation that cn be written in the following form:
\[ a_n(t)y^{(n)}(t) + a_{n-1}(t)+y^{n-1}(t) + . . . + a_1(t)y'(t) + a_0(t)y(t) = g(t) \]
\[ a_n(t)y^{(n)}(t) + a_{n-1}(t)+y^{n-1}(t) + \ldots + a_1(t)y'(t) + a_0(t)y(t) = g(t) \]
Note that $a_n(t)$ does not depeond on any derivative of $y$, so the presence of terms such as $e^y$ or $\sqrt{y'}$ signal that the equation is *nonlinear*.