Re: How to NDSolve the differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg19638] Re: How to NDSolve the differential equation
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Tue, 7 Sep 1999 00:28:35 -0400
• Organization: University of Western Australia
• References: <7qulo3\$2r5@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Chee Lim Cheung wrote:

> I encountered error messages with the tag Power::infy when I tried to do
> the following:
>
> NDSolve[{x y''[x] + Sin[x] y'[x] + 2 x y[x] == 0,y[0]==0, y'[0]==1}, y,
> {x,0,2}]
>
> Can anyone help me in getting Mathematica to produce an answer? I am using
> Mathematica 4.0 & Mathematica 3.0.

The error message gives a hint as to the problem -- and the solution. If you
divide
through by x and replace Sin[x]/x with 1 if x ==0, then NDSolve works fine:

NDSolve[{2 y[x] + If[x == 0, 1, Sin[x]/x] y'[x] + y''[x] == 0,
y[0] == 0, y'[0] == 1}, y, {x, 0, 2}]

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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