View Single Post
 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!