Just your everyday math kid (emoboygenius) wrote in diffeq,
Just your everyday math kid

Dynamics probs

I had a test wednesday and I'm still trying to figure out if i got one of the questions right
it asked to turn a dimensional problem dimensionless
dx/dt = rx -x^3 + x^5

After a lot of screwing with the problem I showed two ways in which I felt it was dimensionless
[x'] = [rx] = [x^3] = [x^5]
this means that x is dimensionless b/c that's the only way [x^3] = [x^5], which also means that r has to be dimensionless
which leads to the entire right hand side, which means the problem is
expanding the right hand side you get
if you look at one of the parenthesis you see x - .5 + ((1+4r)^1/2))/2
using simple logic you know to add these [x] = [.5]
since .5 is dimensionless x is dimensionless
which leads back to the whole line of thought that if x is dimensionless the entire problem is

now, I wouldn't be asking this if I hadnt talked to my prof today and showed him what I did and he looked at me kinda weird and said hmmmm i'll have to look into that and walked off
that and that the left hand side has a dt on it
so yeah, confusion abounds
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