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

**References**:**Is it possible to solve this differential equation?***From:*"Wei Wang" <weiwang@baosteel.com>