MHB Romeo and Juliet initial conditions

[martha1]

Hi all!

I need to give a presentation on a problem in class and @countryboy helped me to figure out most of it, I only have one remaining question.
Here it goes:

Consider the system dr/dt = -j, dj/dt = r , where r (t) represents Romeo’s love (positive values) or hate (negative
values) for Juliet at time t, and j(t) similarly representsJuliet’s feelings toward Romeo

The question I don't really understand is:

(b) Romeo’s and Juliet’s families are enemies. This can be expressed in the initial condition (r, j) = (.,.) at time t = 0.

So I know the answer needs to be (-1,-1), but I don't really get why. I understand the values need to be negative, as they initially hate each other, but why -1 and not for example -1.2?

The solutions I got to answer the remaining questions are:
r(t)= sin(t)-cos(t)
j(t)=-cos(t)-sin(t)

And I used the initial conditions to come to this, but I don't get how I was supposed to know them from the start.
Any explanation would be welcome, thanks!

 

[I like Serena]

Hi all!

I need to give a presentation on a problem in class and @countryboy helped me to figure out most of it, I only have one remaining question.
Here it goes:

Consider the system dr/dt = -j, dj/dt = r , where r (t) represents Romeo’s love (positive values) or hate (negative
values) for Juliet at time t, and j(t) similarly representsJuliet’s feelings toward Romeo

The question I don't really understand is:

(b) Romeo’s and Juliet’s families are enemies. This can be expressed in the initial condition (r, j) = (.,.) at time t = 0.

So I know the answer needs to be (-1,-1), but I don't really get why. I understand the values need to be negative, as they initially hate each other, but why -1 and not for example -1.2?

The solutions I got to answer the remaining questions are:
r(t)= sin(t)-cos(t)
j(t)=-cos(t)-sin(t)

And I used the initial conditions to come to this, but I don't get how I was supposed to know them from the start.
Any explanation would be welcome, thanks!

Hi martha, welcome to MHB! ;)

The initial condition is arbitrary - any negative set of values will do.
(-1,-1) is just the simplest set of values.
Alternatively we might for instance pick $(-\frac 1{\sqrt 2},-\frac 1{\sqrt 2})$, which would put us on the unit circle.