On Wednesday, April 3, 2013 1:51:49 AM UTC+5:30, Manoj Kumar wrote: > > I had been reading this paper by Dr.Starrett and I can very well recall > somewhere in my freshman year about PDE's of this type. > > Fx * a(x, y) + Fy* b(x, y) = c(x, y) > > that can be solved by this method > > dx dy ds > ---- === --------- === -------- > a(x, y) b(x, y) c(x, y) > > where s can be found by just integrating (dx * c(x, y)) / a(x, y) > > 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.
> However, looking at this random example. > > Fx( x* y) + Fy( x**2 * y) = 1 > > This should be solved by: > > dx dy df > ----- === -------- === -------- > (x*y) (x**2 * y) 1 > > > just taking the first and the third part, dx / (x * y) = df , we get f > = ln(x) / y > > However If I substitute it back in the equation, fx = 1 / (x*y) and fy = > -ln(x) / (y**2) , it doesn't seem to add up to one. Am I missing something, > really basic over here? > Regards, Ankit Agrawal, Senior undergrad in EE, IIT Bombay. -- 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.
