On 19/11/2020 15:37, Oscar Benjamin wrote:
I obviously wasn't paying enough attention when I wrote that :)
I know the feeling, because I also managed to garble the differential
equation, which should read:
n**2*f(x) - x*Derivative(f(x), x) + (1 - x**2)*Derivative(f(x), (x, 2))
I am pretty sure that should resolve to a simple differential equation
after the substitution x=cos(t)
I tried to follow your prescription but I think the confusion may have
set in here,
In [233]: xf = Function('x') # make x a function of t
because I guess I don't need xf because the ODE is already represented
in terms of an undefined function f(x).
I also had difficulty following what you were doing once I reached the
nested lambda expressions!
It would be great if you could find the time to demonstrate your method
on my example - a working example is always worth its weight in gold.
When I originally put in this query, I had assumed that there would be a
one-line answer buried in SymPy.
I have also explored my own Python solution to the problem, recursively
processing down the whole ODE expression and picking off the derivatives
as I come across them. It looks feasible, but it isn't finished yet.
I know it is a very busy time for you right now, so if you want to put
this in your pending tray for a week, that is fine :)
David
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