       Re: Solving differential equations with parameters

• To: mathgroup at smc.vnet.net
• Subject: [mg79824] Re: Solving differential equations with parameters
• From: chuck009 <dmilioto at comcast.com>
• Date: Sun, 5 Aug 2007 05:00:32 -0400 (EDT)

```You could "Map" the DE solver "DSolve" onto a list of parameters using a pure function like this:

(DSolve[y'[x] == -Sin[#*x + y[x]], y, x]) & /@ {p1, p2, p3}

Note the place-holder #.  Each element in the list {p1,p2,p3} is inserted there and DSolve executed for each.  The results is a list of solutions.  It's a non-linear equation, Mathematica has to use inverse functions to solve it so I'd be suspicious of the solution so I'd check it by solving it numerically using NDSolve just to make sure.  Just make up any initial conditions and values for p for the numeric check and compare it with the symbolic solution.

> 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?
>
>

```

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