Re: New to mathematica: Question about solving

*To*: mathgroup at smc.vnet.net*Subject*: [mg74694] Re: [mg74664] New to mathematica: Question about solving*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sat, 31 Mar 2007 01:39:19 -0500 (EST)*Reply-to*: hanlonr at cox.net

I must have evaluated out of order. Change this to read soln=DSolve[{y'[x] == y[x] + y[x]^3}, y[x], x] {{y[x] -> -((I*E^(x + C[1]))/ Sqrt[-1 + E^(2*x + 2*C[1])])}, {y[x] -> (I*E^(x + C[1]))/Sqrt[-1 + E^(2*x + 2*C[1])]}} soln=soln/. expr1_*(expr2_)^(-1/ 2):>(expr2/(expr1^2))^(-1/2)/.C[1]:>-Log[C]/2//ExpandAll {{y[x] -> 1/Sqrt[C/E^(2*x) - 1]}, {y[x] -> 1/Sqrt[C/E^(2*x) - 1]}} Bob Hanlon ---- Bob Hanlon <hanlonr at cox.net> wrote: > soln=DSolve[{y'[x] == y[x] + y[x]^3}, y[x], x] > > {{y[x] -> -((I*E^(x + C[1]))/ > Sqrt[-1 + E^(2*x + 2*C[1])])}, > {y[x] -> (I*E^(x + C[1]))/Sqrt[-1 + E^(2*x + 2*C[1])]}} > > soln=soln/.{ > expr1_*(expr2_)^(-1/2):>(expr2/(expr1^2))^(-1/2), > C[1]:>-Log[C]/2}//ExpandAll > > {{y[x] -> 1/Sqrt[C/E^(2*x) - 1]}, > {y[x] -> 1/Sqrt[C/E^(2*x) - 1]}} > > > Bob Hanlon > > ---- traz <t_raz at yahoo.com> wrote: > > Whenever I try to solve differential equations in mathematica, I get a solution with an imaginary part different from the solution in a text book. For example: > > > > DSolve[{y'[x] == y[x] + y[x]^3}, y, x] > > > > will give me a solution that has an imaginary part and not the one I expect here from the text book: > > > > {+(Ce^(-2x)-1)^(-1/2), -(Ce^(-2x)-1)^(-1/2)} > > > > Can anyone give me a tip on how to do this? Also does anyone know of an online tuttorial that goes into details a little bit? > >