Could you help me solve first order diff eq?

  • #1

Main Question or Discussion Point

dv/dt=g-(k/m)*v^2
i thought about all sorts of diff eq solving techniques
but nothing comes up to my mind

dv/(g-(k/m)*v^2)=dt
but it doesnt really help ...
 

Answers and Replies

  • #2
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0
I think it's quite correct, but there could be some errors in calculation..anyway:

http://spiro.fisica.unipd.it/~mimo/altro/sol.JPG [Broken]
 
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  • #3
tiny-tim
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Homework Helper
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hi hangainlover! :smile:

(try using the X2 tag just above the Reply box :wink:)

learn your list of standard integrals from the pf library :wink:
 
  • #4
Delta2
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Separation of variables seems to work. Just try to transform the integral [tex]\int \frac{1}{g-\frac{k}{m}v^2}dv[/tex] to the case xxvi of the standard integrals link provided by tiny-tim.
 
  • #5
HallsofIvy
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Specifically,
[tex]g- \frac{k}{m}v^2[/tex]
, being a "difference of squares", factors as
[tex](\sqrt{g}- \sqrt{k/m}v)(\sqrt{g}+ \sqrt{k/m}v)[/tex]
and so that function can be integrated by "partial fractions".
 

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