def de_dt(e, times, beta, c_0):                             # pragma: no cover
    """Compute eccentricity time derivative

    Computes the evolution of the eccentricity from the emission of gravitational waves following
    Peters & Mathews (1964) Eq. 5.13

    Parameters
    ----------
    e : `float`
        Initial eccentricity

    times : `float/array`
        Evolution timestep. Not actually used in function but required for use with scipy's
        :func:`scipy.integrate.odeint`

    beta : `float`
        Constant defined in Peters and Mathews (1964) Eq. 5.9. See :meth:`legwork.utils.beta`

    c_0 : `float`
        Constant defined in Peters and Mathews (1964) Eq. 5.11. See :meth:`legwork.utils.c_0`

    Returns
    -------
    dedt : `float/array`
        Eccentricity time derivative
    """
    dedt = -19 / 12 * beta / c_0**4 * (e**(-29 / 19) * (1 - e**2)**(3/2)) \
        / (1 + (121/304) * e**2)**(1181/2299)
    return dedt