Re: Is it possible to solve this differential equation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg89028] Re: Is it possible to solve this differential equation?*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Sat, 24 May 2008 03:52:42 -0400 (EDT)*References*: <g15qst$pgd$1@smc.vnet.net>

Wei Wang schrieb: > 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] If I read correctly what your equation is something like ((dy/B) / (A dx) ) == (Sqrt[B/y] - 1) (1 - Exp[-y/B]^(1/2) so with y/B = z, u = A x you have du = dz / (Sqrt[1/z] - 1) * (1 - Exp[-z]^(-1/2) Integrate[dz / (Sqrt[1/z] - 1) * (1 - Exp[-z]^(-1/2),z] gives u==(Sqrt[2*Pi] + 2*E^(z/2)*(Sqrt[E^(-z)] + Sqrt[1/z])*Sqrt[-z] - Sqrt[2*Pi]*Erf[Sqrt[-z]/Sqrt[2]])/ (E^(z/2)*(Sqrt[E^(-z)]*Sqrt[1/z]*Sqrt[-z])) This transcendental equation is solvable for u->z[u] only numerical. Of course, if you are interested in numerical solutions you can NDSolve the original equation directly, too. -- Roland Franzius