Re: Solving differential equations with parameters

*To*: mathgroup at smc.vnet.net*Subject*: [mg79813] Re: Solving differential equations with parameters*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 5 Aug 2007 04:54:50 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <f91j5e$677$1@smc.vnet.net>

Ivan wrote: > Hi, I am trying to solve the differential equations like > > y'[x]= - Sin[ p*x + y[x] ] > > where p is a parameter. Now I want to solve the equation with respect > to x for a range of values of p, instead for just a single p. > What is the best way to do it? Hi Ivan, If I have correctly understood your request, you are looking for an analytic solution. The general solution can be obtain with *DSolve*. For instance, In[1]:= eqn = y'[x] == -Sin[p*x + y[x]]; sol = DSolve[eqn, y, x]; y[x] /. sol[[1]] eqn /. sol[[1]] // FullSimplify Out[3]= 2 -p x + 2 ArcTan[(1 - Sqrt[-1 + p ] 1 2 2 Tan[- (-Sqrt[-1 + p ] x + Sqrt[-1 + p ] C[1])]) 2 / p] Out[4]= True HTH, Jean-Marc