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Add y1 in coin par coeur

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flyingscorpio@arch-desktop 2021-09-20 10:05:38 +02:00
parent 1184f3256a
commit 67ad5ad697
1 changed files with 5 additions and 5 deletions
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analyse/main.tex
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@ -153,11 +153,11 @@
\midrule
\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}{*}{$\lambda, \mu \in \mathbb{R}$} \\
\multirow{3}{*}{$ay'' + by' + cy = 0$} & $\Delta > 0$ & $\lambda e^{r_1 x} + \mu e^{r_2 x} + y_1$ & \multirow{3}{*}{$\lambda, \mu \in \mathbb{R}$, $y_1$ solution particulière} \\
\cline{2-3}
& $\Delta = 0$ & $(\lambda x + \mu) e^{r_0 x}$ & \\
& $\Delta = 0$ & $(\lambda x + \mu) e^{r_0 x} + y_1$ & \\
\cline{2-3}
& $\Delta < 0$ & $e^{\alpha x}(\lambda\cos{(\beta x)} + \mu\sin{(\beta x)})$ & \\
& $\Delta < 0$ & $e^{\alpha x}(\lambda\cos{(\beta x)} + \mu\sin{(\beta x)}) + y_1$ & \\
\bottomrule
\end{tabularx}
@ -368,7 +368,7 @@
La solution générale de $(E)$ s'écrit~:
\begin{equation*}
y = y_0 + y_1
\color{red}{y = y_0 + y_1}
\end{equation*}
\subsection{Équations différentielles du 2\up{nd} ordre}
@ -515,7 +515,7 @@
La solution générale de $(E)$ s'écrit~:
\begin{equation*}
y = y_0 + y_1
\color{red}{y = y_0 + y_1}
\end{equation*}
\clearpage