Python code

# -*- coding: utf-8 -*-
"""
Illustrate the shooting method for the equation
 w'' = 3/2*w**2
The initial values picked for the first derivative are
w'(0) = s = [-40, -36, -10, -8, -7]
"""
from__future__import division
importnumpyasnp
importmatplotlib.pyplotasplt
fromscipy.integrateimport odeint
importseabornassns
sns.set_style("white")
deffunc(y, t):
 return [y[1], 1.5*y[0]**2]
t = np.linspace(0, 1.1, 50)
diff_ini = [-40, -36, -10, -8, -7]
plt.figure(figsize=(6, 4))
for dy in diff_ini:
 y0 = [4, dy] 
 y = odeint(func, y0, t)
 plt.plot(t, y[:, 0], label=r"$s=%i$" % dy)
plt.plot(1, 1, "o", mfc="#3c3c3c")
plt.legend(loc="best")
plt.xlabel(r"$t$")
plt.ylabel(r"$w(t; s)$")
plt.savefig("Shooting_method_trajectories.svg", bbox_inches="tight")
plt.show()