human
Complete the below
def _nonlinear_2eq_order1_type5(func, t, eq):

    ''''Clairaut system of ODEs
    .. math:: x = t x\' + F(x\',y\')
    .. math:: y = t y\' + G(x\',y\')
    The following are solutions of the system
    `(i)` straight lines:
    .. math:: x = C_1 t + F(C_1, C_2), y = C_2 t + G(C_1, C_2)
    where `C_1` and `C_2` are arbitrary constants;
    `(ii)` envelopes of the above lines;
    `(iii)` continuously differentiable lines made up from segments of the lines
    `(i)` and `(ii)`.'
    '''

Can you provide a the Python program you requested?
assistant
#Here is the Python program you requested.
    (C1, C2) = get_numbered_constants(eq, num=2)
    f = Wild('f')
    g = Wild('g')
    def check_type(x, y):
        r1 = eq[0].match((((t * diff(x(t), t)) - x(t)) + f))
        r2 = eq[1].match((((t * diff(y(t), t)) - y(t)) + g))
        if (not (r1 and r2)):
            r1 = eq[0].match(((diff(x(t), t) - (x(t) / t)) + (f / t)))
            r2 = eq[1].match(((diff(y(t), t) - (y(t) / t)) + (g / t)))
        if (not (r1 and r2)):
            r1 = (- eq[0]).match((((t * diff(x(t), t)) - x(t)) + f))
            r2 = (- eq[1]).match((((t * diff(y(t), t)) - y(t)) + g))
        if (not (r1 and r2)):
            r1 = (- eq[0]).match(((diff(x(t), t) - (x(t) / t)) + (f / t)))
            r2 = (- eq[1]).match(((diff(y(t), t) - (y(t) / t)) + (g / t)))
        return [r1, r2]
    for func_ in func:
        if isinstance(func_, list):
            x = func[0][0].func
            y = func[0][1].func
            [r1, r2] = check_type(x, y)
            if (not (r1 and r2)):
                [r1, r2] = check_type(y, x)
                (x, y) = (y, x)
    x1 = diff(x(t), t)
    y1 = diff(y(t), t)
    return {Eq(x(t), ((C1 * t) + r1[f].subs(x1, C1).subs(y1, C2))), Eq(y(t), ((C2 * t) + r2[g].subs(x1, C1).subs(y1, C2)))}