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Re: Is it possible to solve this differential equation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89025] Re: [mg89009] Is it possible to solve this differential equation?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sat, 24 May 2008 03:52:06 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200805230710.DAA25939@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

No, not as it stands, because it has (at least) two syntax errors:

First, there is a missing right parenthesis in the left-hand side of the 
equation; is it supposed to go after the exponent (1/2) or after the 
Exp[-y[x]/B] ?

Second, there is a spurious "=" at the end of your first line; probably 
this is the result of the way you copied the input cell into your e-mail 
client, or the way that client handled a long line.

If the missing parenthesis is to go after the (1/2), then the answer to 
your question is yes, but you probably won't be happy with the 
"solution" that Mathematica (version 6) provides:

   {{y[x] -> InverseFunction[Integrate[(E^(K[1]/(2*B))*Sqrt[K[1]])/
         ((-1 + E^(K[1]/(2*B)))*(Sqrt[B] - Sqrt[K[1]])),
        {K[1], 1, #1}] & ][A*x + C[1]]}}

And if the missing parenthesis is to go after Exp[-y[x]/B], then again 
the answer is yes, but again disappointing:

   {{y[x] -> InverseFunction[Integrate[(E^(K[1]/(2*B))*Sqrt[K[1]])/
         (Sqrt[-1 + E^(K[1]/B)]*(Sqrt[B] - Sqrt[K[1]])),
        {K[1], 1, #1}] & ][A*x + C[1]]}}

Wei Wang wrote:
> Hi,
> 
> Is it possible to solve the following equation?
> 
> DSolve[A (Sqrt[B/y[x]] - 1) (1 - Exp[-y[x]/B]^(1/2) == D[y[x], x], =
> y[x], x]
> 
> Thanks,
> 
> Wei
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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