#### Numeric solve transcendental equation in python or Matlab

``````q(x) = a*x + b + w(x)
``````

Euler-Bernoulli方程：

``````E * I * diff(w(x), x, x, x, x) = q(x)
``````

2 个回复

``````from __future__ import division
from sympy import *
x = symbols('x')
w = symbols('w', cls=Function)
a,b,E,J =  symbols('a b E J')
equ = E*J*diff(w(x),x,4) - a*x -b - w(x)
dsolve(equ, w(x))
# This generates a function that is too generic and too big to copy-paste
# Let's make some assumptions
J = Symbol('J', real=True, positive=True)
E = Symbol('E', real=True, positive=True)
equ = E*J*diff(w(x),x,4) - a*x -b - w(x)
dsolve(equ, w(x))
``````

``````               -x                 x
───────────       ───────────
4 ___ 4 ___       4 ___ 4 ___
╲╱ E ⋅╲╱ J        ╲╱ E ⋅╲╱ J          ⎛     x     ⎞         ⎛     x     ⎞
w(x) = C₁⋅ℯ            + C₂⋅ℯ            + C₃⋅sin⎜───────────⎟ + C₄⋅cos⎜───────────⎟ - a⋅x - b
⎜4 ___ 4 ___⎟         ⎜4 ___ 4 ___⎟
⎝╲╱ E ⋅╲╱ J ⎠         ⎝╲╱ E ⋅╲╱ J ⎠
``````

``````syms q x w(x) a b E I
q = a*x+b+w(x);
sol = dsolve(E*I*diff(diff(diff(diff(w)))) == q)
sol_part = subs(sol,[E I],[2e5 100]) % etc.
``````

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