Help: Differential equation Romeo & Juliet

[Guest]

Hi, I have to make an assignment on differential equations and Romeo and Juliet.
r(t) is romeo's love for Juliet at time t, j(t) is Juliet's love for Romeo at time t
So far, it is given: dr/dt=-j and dj/dt=r.
It is also given that Romeo & Juliet's families are enemies, thus the initial condition at time t=0 is (r,j)=(-1,-1)

If we would take the second derivative of r we get: r’’=-j’. We know that j’=r, which means r’’ =-r. This can be recognized as the equation of an harmonic oscillator. Our solution will therefore have this shape: r=A sin(t)+B cos(t).
To get the solution to j, we know j=-r’, which gives us:
j= -(Acos(t)-Bsin(t))= -Acos(t)+Bsin(t)
With the initial conditions:
r(t)= sin(t)-cos(t)
j(t)=-cos(t)-sin(t)

Now, the last part of the assignment is:
“In the Spring a young man’s fancy lightly turns to
thoughts of love,” says Tennyson. What differential
equation concept is best invoked to capture this
idea?
⇤ a forcing term
⇤ an unstable equilibrium
⇤ a nonlinear function for t
⇤ none of the above

Could someone help me with this part?

[Guest]

It looks to me like it is saying that the differential equations modeling this are incomplete- that there needs to be a time dependent term.

Something like:
[tex]\frac{dr}{dt}= -r+ f(t)[/tex] where f(t) is a periodic function that has its maximum in the spring time.