eth-janishutz/eth-summaries
1
0
Fork 0
mirror of https://github.com/janishutz/eth-summaries.git synced 2025-11-25 18:44:24 +00:00
Code Issues Packages Projects Releases Wiki Activity

[Analysis] Basically catch up to present day

Browse Source
This commit is contained in:
Janis Hutz
2025-10-02 09:55:22 +02:00
parent d8d87c7bd7
commit ef1aff082f
5 changed files with 22 additions and 4 deletions
Download Patch File Download Diff File Expand all files Collapse all files

9
semester3/analysis-ii/parts/diffeq/linear-ode/01_order-one.tex
View File

@@ -1,2 +1,7 @@
\newsection
\subsection{Linear Differential Equations of first order}
\newsectionNoPB
\subsection{Linear differential equations of first order}
\shade{gray}{Finding solution set} \bi{(1)} Find basis $\{ f_1, \ldots, f_k \}$ for $\mathcal{S}_0$ for homogeneous equation (set $b(x) = 0$).
\bi{(2)} If inhom. find $f_p$ that solves the equation. The set of solutions $\mathcal{S}_b = \{ f_h + f_p \divides f_h \in \mathcal{S_0} \}$.
\bi{(3)} If initial conditions, find equations $\in \mathcal{S}_b$ which fulfill conditions using SLE (as always)
\shortproposition Solution of $y' + ay = 0$ is of form $f(x) = z e^{-A(x)}$ with $A$ anti-derivative of $a$