From 10cdca6bd220aa8cf4ae4ff131f809eb9b439285 Mon Sep 17 00:00:00 2001
From: Gerardo Marx <gmarx_cc@itmorelia.edu.mx>
Date: Tue, 9 Jun 2020 23:26:34 -0500
Subject: [PATCH] symbolic ODE and series

---
 readme.md              |  2 ++
 scripts/program-02a.py | 10 ++++++++++
 scripts/program-02b.py | 10 ++++++++++
 scripts/program-02c.py |  9 +++++++++
 4 files changed, 31 insertions(+)
 create mode 100644 readme.md
 create mode 100644 scripts/program-02a.py
 create mode 100644 scripts/program-02b.py
 create mode 100644 scripts/program-02c.py

diff --git a/readme.md b/readme.md
new file mode 100644
index 0000000..5e19599
--- /dev/null
+++ b/readme.md
@@ -0,0 +1,2 @@
+# Dynamical systems examples Lynch
+Repository for examples related with book Dynamical system with applications using Python by Stephen Lynch. 
diff --git a/scripts/program-02a.py b/scripts/program-02a.py
new file mode 100644
index 0000000..1f15c01
--- /dev/null
+++ b/scripts/program-02a.py
@@ -0,0 +1,10 @@
+# Program 02a: A simple separable ODE. See Example 1.
+from sympy import dsolve, Eq, Function, symbols, pprint
+t = symbols('t')
+x = symbols('x', cls=Function)
+dxdt = x(t).diff(t)
+de = Eq(dxdt, -t/x(t))
+print('Program 02a:\n')
+pprint(de)
+sol = dsolve(de, x(t))
+pprint(sol)
diff --git a/scripts/program-02b.py b/scripts/program-02b.py
new file mode 100644
index 0000000..43c753e
--- /dev/null
+++ b/scripts/program-02b.py
@@ -0,0 +1,10 @@
+# Program 02b: The logistic equation; example 4-ch2.
+from sympy import dsolve, Eq, Function, symbols, pprint
+t, b, d = symbols('t beta sigma')
+P = symbols('P', cls=Function)
+dPdt = P(t).diff(t)
+de = Eq(dPdt, P(t)*(b-d*P(t)))
+print('program 02b:\n')
+pprint(de)
+sol = dsolve(de, P(t))
+pprint(sol)
diff --git a/scripts/program-02c.py b/scripts/program-02c.py
new file mode 100644
index 0000000..31dff3b
--- /dev/null
+++ b/scripts/program-02c.py
@@ -0,0 +1,9 @@
+# Program 02c: Power series solution first order ODE; exa 7 chp 2
+from sympy import dsolve, Function, pprint
+from sympy.abc import t
+x = Function('x')
+dxdt = x(t).diff(t)
+ode = dxdt+t*x(t)-t**3
+sol = dsolve(ode, hint='1st_power_series', n=8, ics={x(0): 1})
+print('Solution:\n')
+pprint(sol)