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: <email@example.com>
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^(3/2))) Log[-2 + 2 (C + Sqrt[C] Sqrt[C - 2/y[x]]) y[x]] + ( Sqrt[C - 2/y[x]] y[x])/C)^2 == (x + C)^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