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[Analysis] Update diff eq section

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Janis Hutz
2026-02-02 08:06:40 +01:00
parent 6f362bb388
commit 11d604880c
3 changed files with 5 additions and 5 deletions
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semester3/analysis-ii/cheat-sheet-jh/parts/diffeq/linear-ode/00_intro.tex
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@@ -19,7 +19,7 @@ The solution space $\mathcal{S}$ is spanned by $k$ functions, which thus form a
\shade{gray}{Finding solutions (in general)}
\rmvspace
\begin{enumerate}[label=\bi{(\arabic*)}, noitemsep]
\item Find basis $\{ f_1, \ldots, f_k \}$ for $\mathcal{S}_0$ for homogeneous equation (set $b(x) = 0$) (i.e. find homogeneous part, solve it)
\item If inhomogeneous, find $f_p$ that solves the equation. The set of solutions is then $\mathcal{S}_b = \{ f_h + f_p \divides f_h \in \mathcal{S}_0 \}$.
\item If there are initial conditions, find equations $\in \mathcal{S}_b$ which fulfill conditions using SLE (as always)
\item Find the solution to the homogeneous equation ($b(x) = 0$) using one of the methods below
\item If inhomogeneous, use a method below for an Ansatz for $f_p$, derive it and input that into the diffeq and solve.
\item If there are initial conditions, find equations $\in \cS$ which fulfill conditions using SLE (as always)
\end{enumerate}