FO2.sage

def generator():
    t = var("t")
    y,yp = mi_vars("y","y'")

    # pick n for y=kx^n
    n = randrange(2,6)*choice([-1,1])
    # pick initial value
    t0 = choice([-1,1])
    # pick coefficient
    k = randrange(1,5)*choice([-1,1])
    hom_sol = k*t^n
    # particular solution
    kp = randrange(1,6)*choice([-1,1])
    m = n
    while m==n:
        m = randrange(1,5)*choice([-1,1])
    part_sol = kp*t^m
    ts = n*part_sol-t*part_sol.diff()
    ode = shuffled_equation(ts,t*yp,-n*y)
    ivp_sol = (y==k*t^n+part_sol)
    y0 = k*t0^n+kp*t0^m

    return {
        "ode": ode,
        "t0": t0,
        "y0": y0,
        "ivp_sol": ivp_sol,
    }