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Differential Equations

  • Thread starter Fizz_Geek
  • Start date
  • #1
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Homework Statement



r" = 1/r^2

Homework Equations



A friend gave this to me, he was just wondering how we'd approach it.

The Attempt at a Solution



I don't think the equation is linear, so I don't know how to approach it. My friend suggested integrating both sides with respect to r, but we don't know if that's legal because we don't know what r might be a function of.
 

Answers and Replies

  • #2
hunt_mat
Homework Helper
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Multiple both sides by r' and that will give you the first integral.
 
  • #3
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Multiple both sides by r' and that will give you the first integral.
How's does multiplying by a derivative give me an integral?
 
  • #4
hunt_mat
Homework Helper
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As
[tex]
r''=\frac{1}{r^{2}}
[/tex]
Multiply both sides by r' to obtain:
[tex]
r'r''=\frac{r'}{r^{2}}\Rightarrow\left(\frac{(r')^{2}}{2}\right) '=\left( -\frac{1}{r}\right) '
[/tex]
Integrate easily from here.
 
  • #5
HallsofIvy
Science Advisor
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955
Did you try it? What is the derivative of [itex](r')^2[/itex]? So what is the integral of [itex]r' r''[/itex]? What is the integral of [itex]dr/r^2[/itex]?
 
  • #6
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To hunt_mat:

That's a very nice trick! I got stuck on the next step, integrating (r')2, but I'll try to work that out with my friend before asking again.

Thanks very much!
 
  • #7
hunt_mat
Homework Helper
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It's a standard trick, become familier with it.
 

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