From d56bf4f939d25cea9ac9953b2b0f3237b2dfe8cd Mon Sep 17 00:00:00 2001
From: daHugen <david.hugentobler@ost.ch>
Date: Tue, 19 Jul 2022 18:35:13 +0200
Subject: added some equations and made some changes

---
 buch/papers/lambertw/teil4.tex | 14 ++++++++++----
 1 file changed, 10 insertions(+), 4 deletions(-)

(limited to 'buch/papers/lambertw/teil4.tex')

diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex
index e0f7731..6184369 100644
--- a/buch/papers/lambertw/teil4.tex
+++ b/buch/papers/lambertw/teil4.tex
@@ -237,10 +237,16 @@ Leitet man die Funktion \eqref{lambertw:funkLoes} nach x ab und setzt die Anfang
 	\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}
 	&=
 	\eta \\
-	x\left(t\right)
-	&=
-	\sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\
 	\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}
 	&=
-	\left(\frac{x}{x_0}\right)^2
+	\left(\frac{x}{x_0}\right)^2 \\
+	x\left(t\right)
+	&=
+	\sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}}
 \end{align*}
+\begin{equation}
+	y(t)
+	=
+	\frac{1}{4}\left(\left(y_0+r_0\right)\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}+\left(r_0-y_0\right)\cdot\mathrm{ln}\ \left(\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}\right)-r_0+3y_0\right)
+	\label{lambertw:funkNachT}
+\end{equation}
-- 
cgit v1.2.1

