CC2.sage

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

    # pick a for y'-ay
    a = randrange(1,6)*choice([-1,1])

    # particular solution
    b=a
    while (b==a):
        b = randrange(1,6)
    c = choice([-3,-2,2,3])
    part_sol = choice([
        c*exp(b*t),
        c*exp(a*t)*t,
        c*exp(a*t)*sin(b*t),
        c*exp(a*t)*cos(b*t)
    ])
    d = randrange(2,5)
    ode = shuffled_equation(yp,-a*y,-part_sol.diff()+a*part_sol)*d
    k = randrange(1,6)*choice([-1,1])
    ivp_sol = (k*exp(a*t)+part_sol)
    iv = ivp_sol(t=0)

    return {
        "ode": ode,
        "iv": iv,
        "ivp_sol": ivp_sol,
    }