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Put solution homogène of equa diff du 2nd ordre in coin par coeur

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flyingscorpio@arch-desktop 2021-09-19 13:24:38 +02:00
parent 84ac539b62
commit 2448203965
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analyse/main.tex
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@ -145,13 +145,19 @@
\subsection{Équations différentielles}
\begin{tabularx}{\linewidth}{YYc}
\begin{tabularx}{\linewidth}{lllc}
\toprule
Type d'E.D. & Solutions & \\
\multicolumn{2}{l}{Type d'E.D.} & Solutions & \\
\toprule
$ay' + by = 0$ & $\lambda e^{rx} \quad \text{ avec } r = \frac{-b}{a}$ & $a, b, \lambda \in \mathbb{R}$ \\
\multicolumn{2}{l}{$ay' + by = 0$} & $\lambda e^{rx} \quad \text{ avec } r = \frac{-b}{a}$ & $a, b, \lambda\in\mathbb{R}$ \\
\midrule
$ay' + by = f(x)$ & $y_0 + \lambda e^{rx} \quad \text{ avec } r = \frac{-b}{a}$ & \makecell{$y_0$ solution particulière de $ay' + by = f(x)$ \\ $f$ une fonction et $a, b, \lambda \in \mathbb{R}$} \\
\multicolumn{2}{l}{$ay' + by = f(x)$} & $y_0 + \lambda e^{rx} \quad \text{ avec } r = \frac{-b}{a}$ & \makecell{$y_0$ solution particulière de $ay' + by = f(x)$ \\ $f$ une fonction et $a, b, \lambda\in\mathbb{R}$} \\
\midrule
\multirow{3}{*}{$ay'' + by' + cy = 0$} & $\Delta > 0$ & $\lambda e^{r_1 x} + \mu e^{r_2 x}$ & \multirow{3}{*}{$\lambda, \mu \in \mathbb{R}$} \\
\cline{2-3}
& $\Delta = 0$ & $(\lambda + \mu x) e^{r_0 x}$ & \\
\cline{2-3}
& $\Delta < 0$ & $e^{\alpha x}(\lambda\cos{(\beta x)} + \mu\sin{(\beta x)})$ & \\
\bottomrule
\end{tabularx}