I am solving an ODE with Sympy. The equation is
To solve it, I used this little code, which returns this result.
from sympy import *
from numpy import *
import matplotlib.pyplot as plt
x = symbols('x')
y = Function('y')
f = y(x)
print(f)
edo = Eq(f.diff()+3*x**2*f, 6*x**2)
print(edo)
edoSolve = dsolve(edo, f)
print(edoSolve)
C1*exp(-x**3) + 2
My question is, how can I plot the result with x being a range from 0 to 10?
Firstly it's problematic to combine these two lines:
from sympy import *
from numpy import *
These two libraries define many functions with the same names and mixing those together will lead to problems. For clarity it is better to do something like:
import sympy as sym
import numpy as np
You can only plot a sympy expression if you give numbers for all of the symbols apart from the one that you want to plot against (i.e. x in this example). That means that you need to have a concrete value for the integration constant C1. You can get that by giving an initial conditions (ics) argument to dsolve. Also since dsolve returns an equation you need to choose a side of the equation as the expression that you want to plot. Having done that the sym.plot function will do precisely what you ask for:
In [10]: import sympy as sym
In [11]: sol = sym.dsolve(edo, f, ics={f.subs(x, 0): 1})
In [12]: sol
Out[12]:
3
-x
y(x) = 2 - ℯ
In [13]: sym.plot(sol.rhs, (x, 0, 10))
Out[13]: <sympy.plotting.plot.Plot at 0x7f346de1caf0>
If you want to show solutions for multiple values for C1 together, you could append plots:
from sympy import symbols, Function, Eq, dsolve, plot
x = symbols('x')
y = Function('y')
f = y(x)
edo = Eq(f.diff() + 3 * x ** 2 * f, 6 * x ** 2)
edoSolve = dsolve(edo, f)
plot1 = plot(show=False)
for c1 in range(-5, 6):
plotc1 = plot(edoSolve.subs('C1', c1).rhs, (x, 0, 10), show=False)
plot1.append(plotc1[0])
plot1.show()
