RE: Finding solutions to differential eqns

*To*: mathgroup at smc.vnet.net*Subject*: [mg40114] RE: [mg40091] Finding solutions to differential eqns*From*: "David Park" <djmp at earthlink.net>*Date*: Fri, 21 Mar 2003 02:36:39 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

David, Certainly, but you have to study some Mathematica basics, learn how to use the various brackets, how to write derivatives, how % works, how Functions work, read the Help for DSolve, learn how solutions are returned as rules, and how to convert the rule to a definition of the function that solves your equation. Here is your last equation... Clear[x, c, t]; DSolve[x'[t] == (t - 4)*E^(4*t) + t*x[t], x, t][[1,1]] % /. C[1] -> c x[c_][t_] = Simplify[x[t] /. %] which gives... x -> Function[{t}, -((-4*E^(4*t) + E^(4*t)*t)/ (-4 + t)) + E^(t^2/2)*C[1]] x -> Function[{t}, -((-4*E^(4*t) + E^(4*t)*t)/ (-4 + t)) + E^(t^2/2)*c] -E^(4*t) + c*E^(t^2/2) 1) First the symbols used in the equation were cleared. 2) DSolve solves the differential equation and the first solution was picked out with [[1,1]]. 3) Mathematica solves in terms of a general constant C[1]. But this is an expression so it it replaced with the symbol c. 4) Then the definition for x[c][t] is given. c is a parameter and t is the variable. It is done by writing x[t] and then using the DSolve solution to substitute for x. We can now use the definition. For example... x[1][t] -E^(4*t) + E^(t^2/2) x[1][0.5] -6.25591 Plot[x[1][t], {t, -1, 1}]; The solution does solve the equation. x[c]'[t] == (t - 4)*E^(4*t) + t*x[c][t]//Simplify True David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: David [mailto:davidol at hushmail.com] To: mathgroup at smc.vnet.net Subject: [mg40114] [mg40091] Finding solutions to differential eqns Is there a method where you can get Mathematica to find general solutions for differential equations? For example: [2xt(1 + t)]dx/dt = 1 + x^2 dx/dt = (t/x)e^(-x/t) + x/t and dx/dt = (t - 4)e^4t + tx I have access to version 4.0 Cheers, David