Re: Calculus Problem...
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Re: Calculus Problem...
Thomas J. Hruska -- thruska@tir.com writes:
> Okay, this time I have even stumped my math teacher for 3 days with
this
> Calculus problem. I don't know how in the world to work this one:
> Solve the differential:
> dy/dx = (x^2 + y^2)/(2xy)
This is a differential _equation_. Classically, the study of DE's has
been a sort
of "hit or miss" game -- there are certain ones that are susceptible to
this or that
particular trick. The trend in modern courses in this topic is to study
unifying
principles, but to a large extent solving DE's is still an _art_. And of
course it
is not hard at all to dream up a DE that _no-one_ can solve...
The trick in this case is to introduce an auxiliary variable, with the
substitution
y = ux. the the left side becomes dy/dx= u + x*du/dx . The right side
becomes
(well, you can work it out). The you clean it up and integrate.
The interesting thing is what the _calculator_ (specifically the TI-89
or 92+)
makes of this particular problem. Anyone try it?
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<