kruby/notes-archive
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Catchup 3

Browse Source
This commit is contained in:
Nathan Nguyen
2024-10-02 21:35:48 -05:00
parent 7fc1ab33b4
commit fbccdf1683
2 changed files with 213 additions and 4 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
docs/math/diffeq/1-intro.md
View File

@@ -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*.