I wrote the following problem to solve the Euler-Lagrange equation using
dsolve. But sympy dot not provide me the particular solution of the
Euler-equation, that is, with or without the initial conditions (ics),
sympy give me the same result (the general solution). It seems that sympy
does not take into account the ics provided.
The program:
=========
# -*- coding: utf-8 -*-
from sympy import Symbol, Function, diff
from sympy.calculus.euler import euler_equations
from sympy.solvers.ode import dsolve
from sympy import init_printing
init_printing()
x = Function('x')
t = Symbol('t')
# Integrand
L = 1 + diff(x(t),t)**2
# Euler-Lagrange equation
eq = euler_equations(L, x(t), t)
# Genral solution (without ics)
dsolve(eq[0],x(t))
# Particular solution (the initial conditions (ics) are specified)
s = dsolve(eq[0], x(t), ics = {x(0): 1, x(1): 2})
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