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.
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:
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)
finally like the way you suggested:
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!