python 2nd order ode 1

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.

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