[Maxima] ode2 problem (negative log arguments)
Barton Willis
willisb at unk.edu
Tue Aug 28 22:40:41 CDT 2007
-----maxima-bounces at math.utexas.edu wrote: -----
>To: Maxima at math.utexas.edu
>From: Rupert Swarbrick <rupert.swarbrick at lineone.net>
>Sent by: maxima-bounces at math.utexas.edu
>Date: 08/28/2007 10:36AM
>Subject: [Maxima] ode2 problem (negative log arguments)
>
>Hi!
>
>I was hoping to use ode2 to solve for me the following ode:
>
>'diff(p,x) = 1/(W-x) - ((R-1)/(W-x)-1)*p;
>
>(or at least get it into closed form in a single integral). The values
>for x range over [0,W], which means that the answer ode2 gives from
>
>ode2(%,p,x);
>
>which has %e^log(x-W) in it is not suitable!
I think Maxima's answer is OK. Maybe the following is closer to what you
need:
(%i1) 'diff(p,x) = 1/(W-x) - ((R-1)/(W-x)-1)*p;
(%o1) 'diff(p,x,1)=1/(W-x)-p*((R-1)/(W-x)-1)
(%i2) ode2(%,p,x);
(%o2)
p=%e^((R-1)*log(x-W)+x)*(integrate(%e^(-(R-1)*log(x-W)-x)/(W-x),x)+%c)
(%i3) map('radcan,%);
(%o3) p=((%e^x*integrate(%e^(-x)/(x-W)^R,x)-%c*%e^x)*(x-W)^R)/(W-x)
BW
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