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[Analysis] fix 3.2.1

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RobinB27
2026-01-09 10:41:42 +01:00
parent bb13d25cb3
commit d248e215bb
2 changed files with 1 additions and 1 deletions
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semester3/analysis-ii/cheat-sheet-rb/main.pdf
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semester3/analysis-ii/cheat-sheet-rb/parts/03_diffeq_sol.tex
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@@ -70,7 +70,7 @@ $$
\remark If $\alpha_j = \beta + \gamma i \in \C$ is a root, $\bar{\alpha_j} = \beta - \gamma i$ is too.\\ \remark If $\alpha_j = \beta + \gamma i \in \C$ is a root, $\bar{\alpha_j} = \beta - \gamma i$ is too.\\
To get a real-valued solution, apply: To get a real-valued solution, apply:
$$ $$
e^{\alpha_j x} = e^{\beta x}\left( \cos(\gamma x) + i \sin(\gamma x) \right) e^{\alpha_j x} + e^{\alpha_i x} = e^{\beta x}\left( \cos(\gamma x) + \sin(\gamma x) \right)
$$ $$
\begin{subbox}{Explicit Homogeneous Solution} \begin{subbox}{Explicit Homogeneous Solution}