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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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