To solve the Euler-Lagrange equation I wrote the following problem :
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# -*- 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')
# Intégrande
L = 1 + diff(x(t),t)**2
# Equation d'Euler-Lagrange
eq = euler_equations(L, x(t), t)
# General solution
dsolve(eq[0],x(t))
# Particular solution
dsolve(eq[0], x(t), ics = {x(0): 1, x(1): 2})
-------------------------------------------------------------------------
but sympy do not provides me the particular solution, that is, the result
with or without the initial conditions is the same. It seems that sympy
does not take into account the ics provided
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