Re: DSolve difficulties ...
- To: mathgroup at smc.vnet.net
- Subject: [mg111875] Re: DSolve difficulties ...
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 16 Aug 2010 05:55:49 -0400 (EDT)
You can plot the solution of the implicit equation eqn = DSolve[ y''[x] == 1/(y[x]*y[x]), y[x], x][[1]] /. {C[1] -> c1, C[2] -> c2, y[x] -> y} // FullSimplify (Sqrt[c1]*y*Sqrt[c1 - 2/y] + Log[2*y*(Sqrt[c1]*Sqrt[c1 - 2/y] + c1) - 2])^2/ c1^3 == (c2 + x)^2 Reduce[Cases[eqn, Log[expr_] :> expr, Infinity][[1]] > 0, y, Reals] c1 > 0 && y >= 2/c1 Manipulate[Column[{ eq = (Sqrt[c1]*y*Sqrt[c1 - 2/y] + Log[2*y*(Sqrt[c1]*Sqrt[c1 - 2/y] + c1) - 2])^2/ c1^3 == (c2 + x)^2, ContourPlot[ Evaluate[eq], {x, -4, 4}, {y, 2/c1, 4}, PlotRange -> {{-4, 4}, {.35, 4}}, ImageSize -> 400]}], {{c1, 1}, .75, 5, .05, Appearance -> "Labeled"}, {{c2, 0}, -5, 5, .1, Appearance -> "Labeled"}] Bob Hanlon ---- Helen Read <hpr at together.net> wrote: ============= 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.' I get a perfectly good solution. > OK, that was yesterday, fortunately I didn't close the session. > > However, now when I try the same command, I get a null response. Try it in a fresh session. Remember that Mathematica remembers everything you do in a session, and you might have done something that defined x or y or y[x] in some way. -- Helen Read University of Vermont -- Bob Hanlon