odeint with an array as argument

Question

fallowing this question, I've solved the first two equations obtained dydt as an array and wrote this code for the third one:

#some instants
g=1e-25
k=4.14*(10**-5)
#steps
steps=np.logspace(31.247237,33.35443,490000)

ini_values=[1/np.sqrt(2*k),0.7071067811865476]

def func(var,steps,dydt):
    u=var[0]
    dudt=var[1]
    return [dudt,-((k**2)+(g*abs(dydt)/k))*u]
#make t and u have same dimension
u=np.empty_like(steps)
dudt=np.empty_like(steps)
#set initial values
u[0]=ini_values[0]
dudt[0]=ini_values[1]

this part solves the equation step-by-step; for example in step i we use answers of step i-1 as new initial values.

for i in range(1,len(steps)):
    #new steps
    new_steps=[steps[i-1],steps[i]]
    #solving equation
    sol=odeint(func,ini_values,new_steps,args=(dydt[i],))
    #saving data
    u[i] = sol[1][0]
    dudt[i] = sol[1][1]
    # next initial condition
    ini_values = sol[1]

but it takes too long time to get answer which is not efficient for me because I need to repeat this code like thousand times more, also I don't know even if that gives correct answer or not. Is this code correct? and if it is, is there any way to rewrite it to get answers faster?