Represent a first order differential equation in numpy

Question

I have an equation dy/dx = x + y/5 and an initial value, y(0) = -3.

I would like to know how to plot the exact graph of this function using pyplot.

I also have a x = np.linspace(0, interval, steps+1) which I would like to use as the x axis. So I'm only looking for the y axis values.

Thanks in advance.

Answer 1

Just for completeness, this kind of equation can easily be integrated numerically, using scipy.integrate.odeint.

import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt

# function dy/dx = x + y/5.
func = lambda y,x : x + y/5.
# Initial condition
y0 = -3  # at x=0
# values at which to compute the solution (needs to start at x=0)
x = np.linspace(0, 4, 101)
# solution
y = odeint(func, y0, x)
# plot the solution, note that y is a column vector
plt.plot(x, y[:,0])
plt.xlabel('x')
plt.ylabel('y')
plt.show()