Re: yg = \frac{{d(yv)}}{{dt}}, how to solve this differential equation.

*To*: mathgroup at smc.vnet.net*Subject*: [mg125525] Re: yg = \frac{{d(yv)}}{{dt}}, how to solve this differential equation.*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 17 Mar 2012 02:52:11 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

You presented the differential equation using LaTeX syntax, not Mathematica syntax. This suggest you know essentially nothing about Mathematica. To begin: since multi-character names are allowed in Mathematica, you have to indicate multiplication explicitly, perhaps with just a space, rather than juxtaposition. Thus: y g Second, the Mathematica notation for a function y of a variable t is y[t]. Third, one notation for taking the derivative of a function y of t is just y'[t]. Another is D[y[t], t], and the latter is more convenient for taking the derivative of a product such as that of y v: D[y[t] v[t], t] Now of course velocity is the derivative of position, so you really have there: D[y[t] y'[t], t] You can either let Mathematica figure out what that is or use the Product Rule from calculus: D[y[t] y'[t], t] == (y'[t])^2 + y[t] y''[t] True Note the double-equal sign == for indicating an equation. Finally, use the Mathematica function DSolve to solve a differential equation. In your example, this will be: DSolve[g y[t] == D[y[t] y'[t], t], y[t], t] You probably won't like the pair of solutions you obtain, as they will be expressed as inverse functions of some rather complicated expressions involving complex cube- and sixth-rots of -1 along with elliptic integrals. You may have better luck with tractable solutions if you specify initial conditions, but I doubt it. So you may have to try for numerical solutions, use DSolve. On 3/16/12 7:30 AM, Hongyi Zhao wrote: > Hi all, > > I've a differential equation looks like following: > > yg = \frac{{d(yv)}}{{dt}} > > where, g is gravity acceleration, y is the displacement, and the v is > velocity. Could you please give me some hints by using mathematica to > solve it? > > Best regards -- 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