# Homework Help: Non-dimensionalization of diff. system

1. Dec 20, 2008

### LouiseLøcke

I don't have any experince in normalizing when the equations depend on eachother, so was hoping someone could tell me if what I have done is correct, and if not what the problem is :)

1. The problem statement, all variables and given/known data
I need to non-dimensional the following differential equations.

L1:= dn/dt = (a-b-k*y)*n
L2:= dy/dt = l*n-d*y

to
dN/dT= (D-Y)*N
dY/dT = N-Y
knowing that D = (a-b)/d.

3. The attempt at a solution

n = k[n]*N,
y = k[y]*Y,
t = k[t]*T

L1:= d(k[n]*N))/d(k[t]*T) = (a -b-k*(k[y]*Y)*k[n]*N

L2:= d(k[y]*Y)/d(k[t]*T)= l*(k[n]*N) - d*k[y]*Y

I look at L2 first, and divide with k[y]/k[t] on both sides.

Then I set l= k[y]/(k[n]*k[t]) and d=1/k[t]

getting dY/dT = N-Y

next I look at L1, and divide with k[n]/k[t] on both sides and inserting k[t] = 1/delta ( which I found above)

getting
dN/dT = ((a-b)/(d) - (k*(k[y]*Y))/(d))*N

I now put D = (a-b)/d and k = d/k[y]
getting

dN/dT= (D-Y)*N (which is what I wanted)

Is this the correct way of approaching it?
Thanks Louise

Last edited: Dec 20, 2008