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!
