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MathGroup Archive 2007

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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


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