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A tough DE

  1. Aug 27, 2009 #1
    eq#1) -1/r(d/dr)(r*tao)=0
    eq#2)tao=m(-dv/dr)^n (n is a parameter)

    for v=0 at r=R and v=V and r=kR (k and V are parameters)

    I have no idea how to start this or what is the correct way to start.

    I initially integrated tao to get dtao/dr=m(-dv/dr)^n-1, but this just complicates things further with the n-1. Next i plugged in tao into the first equation and then used the product rule so -1/r(d/dr)(r*m(-dv/dr)^n)=0 once again i get the n-1 factor. Then i tried taking the derivative of #1 with respect to r to yield -(1*tao)/r=0. Please could someone please guide me in the right steps!!!
     
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  3. Aug 28, 2009 #2

    HallsofIvy

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    So your equations are:
    [tex]-\frac{1}{r}\frac{dr\tau}{dr}= 0[/tex]
    and
    [tex]\tau= m\left(\frac{dv}{dr}\right)^n[/tex] ?

    Well, multiplying by -r, the first equation is just [tex]\frac{d r\tau}{dr}= 0[/tex] so that [itex]r\tau[/itex]= constant and
    [tex]\tau= \frac{C}{r}[/tex]
    Then the second equation becomes
    [tex]\frac{C}{r}= m\left(\frac{dv}{dr}\right)^n[/tex]
    so
    [tex]\left(\frac{dv}{dr}\right)^n= \frac{C}{mr}[/tex]
    [tex]\frac{dv}{dr}= \frac{C^{1/n}}{m^{1/n}r^{1/n}}[/tex]
    [tex] dv= \left(\frac{C}{m}\right)^{1/n} r^{-1/n}dr[/tex]
    and integrate.
     
  4. Aug 28, 2009 #3
    Thank you Hallsofivey!!!:cool:
     
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