Hi Manoj, "just taking the first and the third part, dx / (x * y) = df , we get f = ln(x) / y"
Now that you explicitly point out difference between dx and dhox, you have integrated 1/xy w.r.t x assuming that y is a constant here(This, coupled with fact that I was awake for 22 hrs, generated my previous response), which is not case as dy/dx = x (as deduced from the first and second part). > >>> Hi Manoj, you might want to check this method, because if you directly >> substitute Fx = df/dx = c(x,y)/a(x,y) and Fy = df/dy = c(x,y)/b(x,y), you >> get LHS = 2*c(x,y). You can take a look at >> http://geo.hmg.inpg.fr/loret/enseee/maths/enseee-maths-IBVPs-3.pdf , >> which discusses the solution of the pdes of this type based on their >> classification. >> >> >> Thank you for pointing me to a source that, discusses the solution to >> pdes, based on their classification. However I'm afraid my question remains >> unanswered for the following reasons. >> > > > Firstly, I think (I may be wrong) df / dx is equal to (dhof / dhox) (I > don't know how to write it here), only if f is a function of x, if not df = > (dhof / dhox) * dx + (dhof / dhoy) * dy , since f is a function of x and y, > so I suppose df / dx cannot be substituted back in the equation. > > You are absolutely right. df/dx, in a general case is not equal dhof/dhox. They are equal in cases where y and x are independent everywhere i.e. dy/dx = 0 and other complicated cases. > Secondly, I would like to cite this example in the research paper, by Dr. > Starrett( Aaron's professor indeed ) Lie > Groups<http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDEQFjAA&url=http%3A%2F%2Feuler.nmt.edu%2F~jstarret%2F05-649LieGroupODEFinalVersion.pdf&ei=WxdcUb65L4OErQeQz4HoAQ&usg=AFQjCNE9ugXh9NmZVLxq9LB8fpYuo6vusA&sig2=HLQVAGHySZ3PndKBIPECdA&bvm=bv.44697112,d.bmk>. > On page 16, he mentions clearly that to solve the equation, sx ξ + sy η = > 1. > > It can be done by, ds = integral (dx / ξ) , I thought this might be for a > case where only ξ is a function of x, but he goes on to say on page 20 that > when ξ is equal to y, s would remain (x / y) . Sorry for being a bit > bookish here, but I hope my point is being put across. > > It would be really helpful, if Aaron or other people here with a much > better mathematical background than me over here, could show me the way > ahead. > -- > Regards, > Manoj Kumar, > Mech Undergrad. > BPGC > Blog <http://manojbits.wordpress.com> > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy?hl=en-US. For more options, visit https://groups.google.com/groups/opt_out.
