Q_9_B_BVP_Using Scipy

Q_9_B_boundary_value_problem.py

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+import numpy as np
+from scipy.integrate import solve_bvp
+import matplotlib.pyplot as plt
+
+def ode(x, y):
+    y1, y2 = y  #y1=y  ,y2=y'
+    dydx = [y2, y2 * np.cos(x) - y1 * np.log(y1)]  #define derivitive
+    return dydx
+# define boundary condition
+def bc(ya, yb):
+    return np.array([ya[0] - 1, yb[0] - np.exp(1)])
+
+# Define the range of x values where we want to solve the ODE
+x = np.linspace(0, np.pi/2, 100)
+
+# Initial guess for the solution
+y_guess = np.zeros((2, x.size))
+
+# Solve the boundary value problem
+sol = solve_bvp(ode, bc, x, y_guess)
+
+# Plot the solution
+plt.plot(sol.x, sol.y[0], label='y(x)')
+plt.xlabel('x')
+plt.ylabel('y')
+plt.title('Solution of y\'\' = y\' * cos(x) - y * ln(y)')
+plt.legend()
+plt.grid()
+plt.show()