[sympy] Help to resolve error in the ODE dsolve method for asymmetrical force of a system

[SOUVIK CHAKRABORTY]

from sympy import *
t=symbols('t',real=True)
x=Function('x')(t)

dx=x.diff(t)
d2x=x.diff(t,2)

w0,a,F1,F2,w1,w2,p=var(r'\omega_0^2 \alpha F_1 F_2 \omega_1 \omega_2 \phi ')
eqA=Eq(d2x,-(w0*x+a*x**2)+F1*cos(w1*t)+F2*cos(w2*t+p))
display(eqA)

𝑑2𝑑𝑡2𝑥(𝑡)=𝐹1cos(𝜔1𝑡)+𝐹2cos(𝜔2𝑡+𝜙)−𝛼𝑥2−𝜔20𝑥

s1=dsolve(eqA)
display(s1)

𝑥(𝑡)=𝐶1+𝐶2𝑡−𝐹1cos(𝜔1𝑡)𝜔21−𝐹2cos(𝜔2𝑡+𝜙)𝜔22+𝑡2𝑥(−𝛼𝑥−𝜔20)2


M=eqA.subs({F1:0.1,F2:0.06,w0:1,a:0.05,w1:0.8,w2:0.9,p:0})
display(M)

𝑑2𝑑𝑡2𝑥(𝑡)=−0.05𝑥2−𝑥+0.1cos(0.8𝑡)+0.06cos(0.9𝑡)


s2=dsolve(M, ics={x.subs(t,0): 0.1, x.diff(t).subs(t,0):0})
display(s2)

--------------------------------------------------------------------------- 
ValueError Traceback (most recent call last) Input In [63], in <cell line: 
1>() ----> 1 s2=dsolve(M, ics={x.subs(t,0): 0.1, x.diff(t).subs(t,0):0}) 2 
display(s2) File 
D:\Programs\Python\Anaconda\lib\site-packages\sympy\solvers\ode\ode.py:605, 
in dsolve(eq, func, hint, simplify, ics, xi, eta, x0, n, **kwargs) 602 
given_hint = hint # hint given by the user 604 # See the docstring of 
_desolve for more details. --> 605 hints = _desolve(eq, func=func, 606 
hint=hint, 
simplify=True, xi=xi, eta=eta, type='ode', ics=ics, 607 x0=x0, n=n, **kwargs) 
608 eq = hints.pop('eq', eq) 609 all_ = hints.pop('all', False) File 
D:\Programs\Python\Anaconda\lib\site-packages\sympy\solvers\deutils.py:209, 
in _desolve(eq, func, hint, ics, simplify, prep, **kwargs) 205 # Magic that 
should only be used internally. Prevents classify_ode from 206 # being 
called more than it needs to be by passing its results through 207 # 
recursive calls. 208 if kwargs.get('classify', True): --> 209 hints = 
classifier(eq, func, dict=True, ics=ics, xi=xi, eta=eta, 210 n=terms, x0=x0, 
hint=hint, prep=prep) 212 else: 213 # Here is what all this means: 214 # 
(...) 223 # hint. 224 # order: The order of the DE, as determined by 
ode_order(). 225 hints = kwargs.get('hint', 226 {'default': hint, 227 hint: 
kwargs['match'], 228 'order': kwargs['order']}) File 
D:\Programs\Python\Anaconda\lib\site-packages\sympy\solvers\ode\ode.py:1016, 
in classify_ode(eq, func, dict, ics, prep, xi, eta, n, **kwargs) 1013 raise 
ValueError("Invalid boundary conditions for Function") 1015 else: -> 1016 
raise ValueError("Enter boundary conditions of the form ics={f(point): 
value, f(x).diff(x, order).subs(x, point): value}") 1018 ode = 
SingleODEProblem(eq_orig, func, x, prep=prep, xi=xi, eta=eta) 1019 
user_hint = kwargs.get('hint', 'default') ValueError: Enter boundary 
conditions of the form ics={f(point): value, f(x).diff(x, order).subs(x, 
point): value} 

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