Re: DSolve difficulties ...

*To*: mathgroup at smc.vnet.net*Subject*: [mg111843] Re: DSolve difficulties ...*From*: Helen Read <hpr at together.net>*Date*: Sun, 15 Aug 2010 07:36:46 -0400 (EDT)*References*: <i45rdj$g3o$1@smc.vnet.net>

On 8/14/2010 6:33 AM, Slide wrote: > Yesterday I typed in the following command line, into the student > version of Mathmatica . > > DSolve[y''[x] == 1/(y[x]*y[x]), y[x], x] > > and got a complicated Solve command and expression back with the > comment 'The equations appear to involve the variables to be solved > for in an essentially non-algebraic way.' Adding to my previous post: OK, the solution to DSolve comes out like this: Solve[((1/(C[1]^(3/2))) Log[-2 + 2 (C[1] + Sqrt[C[1]] Sqrt[C[1] - 2/y[x]]) y[x]] + ( Sqrt[C[1] - 2/y[x]] y[x])/C[1])^2 == (x + C[2])^2, y[x]] That is, Mathematica is able to solve the differential equation, but the solution is given implicitly, rather than solved for y[x]. It got to the part where it wants to solve for y[x] in terms of x, can't do it, and quits there. If you then evaluate the output (the Solve[ ] ), you will get the message about "essentially non-algebraic" which is Mathematica's way of saying it cannot solve the equation explicitly. (It would have to begin with, if it could.) -- Helen Read University of Vermont