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

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
first:
[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
second:
expanding the right hand side you get
-x(x-(1+(1+4r)^1/2)/2)(x-(1-(1+4r)^1/2)/2)
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
oi
so yeah, confusion abounds
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