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MathGroup Archive 2005

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Re: solving simultaneous coupled differential equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62704] Re: solving simultaneous coupled differential equations
  • From: dh <dh at metrohm.ch>
  • Date: Fri, 2 Dec 2005 05:53:03 -0500 (EST)
  • References: <dmlvm8$m95$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
here is a simple example:
we replace one 5th order lin DEQ by 5 first order lin DEQ:

we have
y'''''[x] == 0
for testing, the solution of this is
y[x]= c0 + c1 x + x2 x^2 + c3 x^3+c4 x^4

from this we can get 5 coupled lin DEQ by replacing derivatives by new 
functions
y by y0
y' by y1
..
y'''' by y4

with this we get the following 5 lin DEQ:
eq={
       y0'[x]==y1[x],
       y1'[x]==y2[x],
       y2'[x]==y3[x],
       y3'[x]==y4[x],
       y4'[x]==0
       };
this can be solved like this:
var = {y0, y1, y2, y3, y4};
DSolve[eq, var, x]
this yields for y0:
C[1] + x*C[2] + (x^2*C[3])/2 + 35*C[4] +
  (x^3*C[4])/6 + 15*(C[3] + x*C[4]) +
  5*(C[2] + x*C[3] + (x^2*C[4])/2)
note that the constants are different ci != c[i] but we can verify that 
this has the above form by:
Collect[...,x]

Daniel

akgsh at yahoo.com wrote:
> Hi,
> i am trying to solve 5 coupled first order differential equations.is
> there any way to solve this using mathematica.please help with
> necessary steps.
> thanks
> kumar
> 


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