From c0b2d7b11aa1e1ce04d2187538da9f4f4d21c7d3 Mon Sep 17 00:00:00 2001
From: Michael Wimmer <m.t.wimmer@tudelft.nl>
Date: Sun, 13 Sep 2020 22:06:18 +0200
Subject: [PATCH] remove explicit conversion to linear system
---
src/8_differential_equations_2.md | 23 -----------------------
1 file changed, 23 deletions(-)
diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md
index b8601b0..5286847 100644
--- a/src/8_differential_equations_2.md
+++ b/src/8_differential_equations_2.md
@@ -153,29 +153,6 @@ $$f(x) = e^{\lambda_1 x}, \ x e^{\lambda_1 x} , \ \cdots, \ x^{m_{1}-1} e^{\lamb
$$y'' + Ey = 0.$$
- Let us reduce this second order equation to a system of two first order
- equations. Define
-
- $$y_1=y$$
- $$y_2=y'.$$
-
- Writing $**y**= \begin{bmatrix}
- y_1 \\
- y_2 \\
- \end{bmatrix}$, the DE can be written,
-
- $$\dot{**y**} = \begin{bmatrix}
- y_2 \\
- -E y_1 \\
- \end{bmatrix}$$
- $$\dot{**y**} = \begin{bmatrix}
- 0 & 1 \\
- -E & 0 \\
- \end{bmatrix} \begin{bmatrix}
- y_1 \\
- y_2 \\
- \end{bmatrix}.$$
-
The characteristic polynomial of this equation is
$$P(\lambda) = \lambda^2 + E.$$
--
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