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[Analysis] Start constant coefficients section

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Janis Hutz
2025-10-06 13:07:17 +02:00
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semester3/analysis-ii/analysis-ii-cheat-sheet.pdf
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semester3/analysis-ii/parts/diffeq/linear-ode/01_order-one.tex
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\bi{(3)} If initial conditions, find equations $\in \mathcal{S}_b$ which fulfill conditions using SLE (as always) \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 $a$ \shortproposition Solution of $y' + ay = 0$ is of form $f(x) = z e^{-A(x)}$ with $A$ anti-derivative of $a$
\TODO Improve procedure with notes from session \& SPAM

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semester3/analysis-ii/parts/diffeq/linear-ode/02_constant-coefficient.tex
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\newsectionNoPB \newsectionNoPB
\subsection{Linear differential equations with constant coefficients} \subsection{Linear differential equations with constant coefficients}
The coefficients $a_i$ are constant functions of form $a_i(x) = k$ with $k$ constant. The coefficients $a_i$ are constant functions of form $a_i(x) = k$ with $k$ constant, where $b(x)$ can be any function.\\
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\shade{gray}{Solving:} \bi{(1)} Find \textit{characteristic polynomial} (of form $\lambda^k + a_{k - 1} \lambda^{k - 1} + \ldots + a_1 \lambda + a_0$ for order $k$ lin. ODE with coefficients $a_i$).
Find the roots of polynomial.