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MathGroup Archive 2004

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what is the general theory of extracting solutions from DSolve (and similar) functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45553] what is the general theory of extracting solutions from DSolve (and similar) functions
  • From: nma124 at hotmail.com (steve_H)
  • Date: Tue, 13 Jan 2004 04:04:06 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

hello,

I am learning Mathematica (Mathematica 5.0) and I am having hard time finding 
a general method that works everytime to extract solutions 
from output of DSolve and other Mathematica functions that generates 
solutions in the same format.

I have seen examples that work when the solution contains 
only one result.

I have read that the output of DSolve is in triple nested 
format.

I have seen examples that Flattens the output of DSolve before doing
anything on it to remove the extra nesting.


Now, Assuming I want to do this in a script (i.e. without looking 
at the output of DSolve), so I need to assume there is more 
than one solution.

I tried to write

   [r,c]=Dimensions[sol] 

to see how many solutions there are, but this failed when there is only one 
solution. (sol above is the result of calling DSolve).

I've seen things written like this:

sol = DSolve[{y'[x] == a y[x], y[0] == 1}, y[x], x] 
y = First[y[x] /. sol]

but this assume there is one solution. right?

I am interested in plotting all the solutions, so I guess I need to
have a loop that extracts each solution in turn from the output 
of DSolve and plots each in turn. 

is there a good way to do this? A general generic approach which 
works everytime regardless of the number of solutions?

thanks,
Steve


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