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MathGroup Archive 2006

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Re: General--Differential equation problem..

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66303] Re: General--Differential equation problem..
  • From: "Scout" <Scout at nodomain.com>
  • Date: Mon, 8 May 2006 00:46:56 -0400 (EDT)
  • References: <e3jttb$94n$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

<randomtalk at gmail.com>
news:e3jttb$94n$1 at smc.vnet.net...
> hello, i was trying to solve a set of differential equations needed for a 
> school project.. However, i'm completely new to mathematica 5.0, and i 
> have downloaded trial, here is what i inputed into the software:
>
> In[2]:=
> DSolve[{x'[s] == Cos[z], y'[s] == Sin[z], z'[s] == 1/r, r == 2}, {x, y, 
> z}, s]
>
> returns this error: DSolve::dvnoarg: The function z appears with no 
> arguments.
>
> Is there anything wrong with what i inputed? The differential equations 
> came from this website: http://fy.chalmers.se/LISEBERG/eng/loop_pe.html
>
> Link to the forum page for this post:
> http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=Special:Forum_ViewTopic&pid=10212#p10212
> Posted through http://www.mathematica-users.org [[postId=10212]]
>
>
Hi,
in your set of coupled differential equations, you have forgotten to add the 
independent variable s to the function z.
The  r == 2  equation causes an error inside DSolve[], because it's not a 
differential equation.
Try this:
In[1]:= diff=DSolve[{x'[s] == Cos[z[s]], y'[s] == Sin[z[s]], z'[s] == 1/r}, 
{x[s], y[s], z[s]}, s]

Out[1]= {{z[s] -> s/r + C[1],

                x[s] -> C[2] + r*Cos[C[1]]*Sin[s/r] + r*Cos[s/r]*Sin[C[1]],

                y[s] -> C[3] - r*Cos[s/r]*Cos[C[1]] + 
r*Sin[s/r]*Sin[C[1]] }}

In[2]:= diff /. r->2

Out[2]= {{z[s] -> s/2 + C[1],

                x[s] -> C[2] + 2*Cos[C[1]]*Sin[s/2] + 2*Cos[s/2]*Sin[C[1]],

                y[s] -> C[3] - 2*Cos[s/2]*Cos[C[1]] + 
2*Sin[s/2]*Sin[C[1]] }}



Regards,

    ~Scout~






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