Problems with plotdf



Sorry,

y is a function of x and e and I guess I should have said that.  I was going to try plotdf for fixed values of y but I guess it can't be done that way.  Basically it's a 2d implicit function of y = constant = f(x,e)

It is better said this way using normal coordinate letters 

'diff(z(x,y),x,2)+x^4*z(x,y)=y*z(x,y) 

for a fixed constant 

c = z(x,y)

which means it is a system of equations not just one and z(x,y) is not really known so I was trying to get the plot without solving the diff eq for z and figuring out the form of z(x,y).

Rich





 ------------Original Message------------
From: "S. Newhouse" <sen1 at math.msu.edu>
To: "Richard Hennessy" <rvh2007 at comcast.net>
Cc: "Walter Wegscheider" <walter.wegscheider at ph-noe.ac.at>, "maxima at math.utexas.edu" <maxima at math.utexas.edu>
Date: Fri, Jun-20-2008 3:58 PM
Subject: Re: [Maxima] Problems with plotdf

Richard Hennessy wrote:
> Actually I think I meant if the diff eq was
>
> 'diff(y,x,2)+x^2*y=e*y
>
> 'diff(y,x,2)+x^4*y=e*y
>
> I want to see the direction field of de/dx if that is possible.
>
> Rich
>
>
I don't understand your ODE. Is e supposed to be a function of x?

Also, even if e were a constant, you have a second order equation with 
independent variable x and dependent variable y, and writing (say the 
second one ) as
y'' = e^y - x^4*y

to do 'direction fields' you would have to write it as three dimensional 
system and take short line segments in the directions of the associated 
vector field. The routine plotdf only works with 2d autonomous systems. 
This includes the case of first order 1d non-autonomous systems, since 
they can be made into 2d autonomous systems.

-sen