How to use a function and its derivative('s) to solve another differential equation in python?

Question

I need to solve this two equations simultaneously in python : "b" is constant; but I don't know how to put the function "P" and its derivative at same time in the second equations code, is there anyone could help me?

edition: I have wrote this code to solve the question, but I don't know it is correct or not. is this code correctly gives the answer of those equations?

import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import scipy.integrate as sy
import sys
import numpy as np
np.set_printoptions(threshold=sys.maxsize)
import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt
b=2
def eq(t,u):
    #u[0] is p and u[1] is p', u[2]=y, u[3]=y'.
    u[1]=u[0]*np.sqrt(0.25*(u[0]**-4)*(u[0]+(1/7)+0.7)
    return [u[0],u[1],u[3],-3*(u[1]/(b*u[0]))*u[3] - u[2]]
u0 = [0.00001,0.00001,1.22*(10**28),0]
t = np.linspace(0.0000000001,0.6924*10**33,10000)
sol=solve_ivp(eq,t,u0,None)