       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 + x*C + (x^2*C)/2 + 35*C +
(x^3*C)/6 + 15*(C + x*C) +
5*(C + x*C + (x^2*C)/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