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fatimajan
fatimajan is offline
#12
Aug20-10, 08:03 AM
P: 16
Hi, Dickfore
but I don't think everything else is correct:
Like I said I think you mean u^(-1/2)*P ->P NOT u^(1/2)*P ->P
otherwise the equation doesn't have one term less.
so, dx/du=u^(1/2)*P^(-1)

then like you said dx/du contains an irrational function. Therefore, we can rewrite in the form: u^(1/2)*d/du=A*d/dv
but according to what I said we'll have:

dx/dv=2*v^2/P

so I think we should write:

u^(-1/2)d/du=Ad/dv =>v=2/3*A*u^(3/2) ,A=3/2, =>u=v^(2/3)
so dP/dv=2/3*v^(-1/3)*[bP+nv^(2/3)*(v^(2/3)-c)]/abP

Then dx/dv=2/(3P)

finally like the way you suggested:

dx/dt=dv/dt*dx/dv=abP*2/(3P)=(2/3)ab

the autonomous system of 2 first order ODEs transforms to:
dv/dx=P (3P/2 -> P) and dP/dx=v^(-1/3)/a*[P+(n3/2b)v^(2/3)*(v^(2/3)-c)]

what do you think? was I right?

by the way, I don't know how I can type better like you, you really write clearly. excuse me!