Jason Grout wrote:
> David Joyner wrote:
>> Its exact, so you can do this:
>>
>> sage: x = var("x")
>> sage: y = function("y",x)
>> sage: M = x-y
>> sage: N = -x+y^2
>> sage: desolve(diff(y,x)==-M/N,y)
>> 1/2*x^2 + 1/3*y(x)^3 - x*y(x) == c
>>
>
> Ah, right; thanks for the great reply. However, if I define y as a
> function of x, then checking exactness (another part of this student
> worksheet) doesn't work very well:
>
> sage: diff(M,y)
> Traceback (most recent call last):
> ...
> TypeError: argument symb must be a symbol
>
This is what I settled on. Apparently maxima doesn't solve symbolic
partial differential equations, which is I guess what I was really
looking for here.
var('x,y')
F=vector([x-y, -x+y^2])
M,N=F
My=diff(M,y)
Nx=diff(N,x)
yfun=function('yfun',x)
solution=desolve(diff(yfun,x)==(-M/N).subs(y=yfun),yfun).subs_expr(yfun==y)
potential=solution.lhs()-solution.rhs()
from sage.misc.html import math_parse as mp
html.table([
[mp("$(M,N)$"), (M,N)],
[mp("$(M_y,N_x)$"), (My,Nx)],
[mp("Check $M_y=N_x$"),bool(My==Nx)],
[mp("$\int M dx$"), integrate(M,x)],
[mp("$\int N dy$"), integrate(N,y)],
[mp("Potential (where c is a constant)"), potential],
])
Thanks,
Jason
--
Jason Grout
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