# python 2nd order ode

def dU_dx(U, x): # Here U is a vector such that y=U[0] and z=U[1]. This function should return [y', z'] return [U[1], -2*U[1] - 2*U[0] + np.cos(2*x)] U0 = [0, 0] xs = np.linspace(0, 10, 200) Us = odeint(dU_dx, U0, xs) ys = Us[:,0]

**Here is what the above code is Doing:**

1. We define a function dU_dx that takes in a vector U and a scalar x and returns a vector [y’, z’].

2. We define a vector U0 = [0, 0] that represents the initial conditions y(0) = 0 and z(0) = 0.

3. We create a numpy array xs that represents 200 linearly spaced points between 0 and 10.

4. We use the odeint function to solve the system of differential equations defined by dU_dx, with initial conditions U0, at the points in xs.

5. We create a new numpy array ys that contains only the first element of each row of Us.