       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:=
eqn = y'[x] == -Sin[p*x + y[x]];
sol = DSolve[eqn, y, x];
y[x] /. sol[]
eqn /. sol[] // FullSimplify

Out=
2
-p x + 2 ArcTan[(1 - Sqrt[-1 + p ]

1              2                 2
Tan[- (-Sqrt[-1 + p ] x + Sqrt[-1 + p ] C)])
2

/ p]

Out=
True

HTH,
Jean-Marc

```

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