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Add alpha and beta to coin par coeur

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flyingscorpio@arch-desktop 2021-09-20 10:46:28 +02:00
parent 08144275ed
commit c23297c234
1 changed files with 1 additions and 1 deletions
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analyse/main.tex
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@ -153,7 +153,7 @@
\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}{*}{$ay'' + by' + cy = 0$} & $\Delta > 0$ & $\lambda e^{r_1 x} + \mu e^{r_2 x} + y_1$ & \multirow{3}{*}{$\lambda, \mu \in \mathbb{R}$, $y_1$ solution particulière} \\
\multirow{3}{*}{$ay'' + by' + cy = 0$} & $\Delta > 0$ & $\lambda e^{r_1 x} + \mu e^{r_2 x} + y_1$ & \multirowcell{3}[0pt][c]{$\lambda, \mu \in \mathbb{R}$, $y_1$ solution particulière \\ $\alpha = \frac{-b}{2a} \quad \beta = \frac{\sqrt{|\Delta|}}{2a}$} \\
\cline{2-3}
& $\Delta = 0$ & $(\lambda x + \mu) e^{r_0 x} + y_1$ & \\
\cline{2-3}