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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. 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)

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?

idea?

A. a forcing term

B. an unstable equilibrium

C. a nonlinear function for t

D. none of the above

Could someone help me with this part? I know the answer is A, but I’m not completely sure why.