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Re: Finding branches where general solution is possible

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131943] Re: Finding branches where general solution is possible
  • From: Narasimham <mathma18 at gmail.com>
  • Date: Mon, 4 Nov 2013 23:17:39 -0500 (EST)
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.....
> > 
> > Setting si=x and si' = v
> > 
> > v' /((1 + v) (1 + 2 v)) = Cot[x]
> > 
> Integrate[1/((1 + v) (2 + v)), v] ==
> Integrate[Cot[x], x]
> 
> Integrate[1/((1 + v) (2 + v)), v] ==
> Integrate[Cot[x]/v, x]
> 
> Regards
> Narasimham

Further on, by hand calculation..

Integrate[v/((1 + v) (2 + v)), v] == Integrate[Cot[x], x]

(1+v)/sqrt(1+ 2 v) = sin[si[t]]*const.

q = (1+vi)/sqrt(1+ 2 vi),constant at boundary si=Pi/2.

Let P = P[t]= q sin[si];

si'[th]= (P^2-1)+ P Sqrt[P^2-1]

may be difficult to get general solution this way it appears.

Does Mathematica have a work around for this?

Regards
Narasimham



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