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