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MathGroup Archive 1999

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Re: O.D.E in Power Series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18301] Re: O.D.E in Power Series
  • From: "Atul Sharma" <mdsa at musica.mcgill.ca>
  • Date: Fri, 25 Jun 1999 22:24:10 -0400
  • References: <7ku0dk$9a1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

You might want to check out the following site:

http://www.ma.umist.ac.uk/kd/ode/3x/ref/snuapp/node8.htm#SECTION001700000000
00000000

It is the entry on method SeriesForm for the package ODE.m, also available
at the authors site. This excellent package accompanies the book
Introduction to Ordinary Differential Equations by Gray, Mezzino and Pinsky,
expanding the functionality of the built in DSolve command.

For example, I ran your question through it's ODE function, specifying a
solution using Method->SeriesForm. The answer

In[14]:= ODE [y''[x]-2(x+3)y'[x]-3y[x]==0,y,x,Method->SeriesForm]

Out[14]:= y ->(1 + 3x^2/2 +3 x^3 +43 x^4/8 +39 x^5/5) C[1] + (x+3 x^2+41
x^3/6+12 x^4 +699 x^5 /40) C[2]

Although setting up the series solution is straight forward, there have been
a number of times that loading the ODE package has justified the cost of
this text for me. The code is also available and well documented.

A. Sharma


ALAN S BLOOM wrote in message <7ku0dk$9a1 at smc.vnet.net>...
>I am trying to solve this equation below:
>y''-2(x+3)y'-3y=0 with the DSolve command.
>
>DSolve [y''[x]-2(x+3)y'[x]-3y[x]==0,y[x],x]
>
>How can I make it work?
>
>Alan
>
>




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