symbolic ODE and series

readme.md

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+# Dynamical systems examples Lynch
+Repository for examples related with book Dynamical system with applications using Python by Stephen Lynch. 

scripts/program-02a.py

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+# 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)

scripts/program-02b.py

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+# 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)

scripts/program-02c.py

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+# 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)