Jürgen Tischer <jtischer@emcali.net.co> writes:
> On Friday 19 April 2002 12:45, you wrote:
> >
> > More of one of those subtle limitations of desolve.
> > Desolve uses the LaPlace transform to solve odes, so it really only
> > works well for linear odes.
> >
> > Jay
> > _______________________________________________
>
> Not even for linear ones, Jay,
Oops, there goes that theory :(
Since the LaPlace transform will turn derivatives y'(x), etc., into
products xY(x)-y(0), etc., it can be used to turn a differential
equation into a non-differential equation; unfortunately, the LaPlace
transform will turn products xy(x) into derivatives -Y'(x). So if
the original ode has the unknown function being multiplied by the
variable, it just gets turned into another ode. Not very useful.
So desolve really only works with linear odes with constant
coefficients.
> (C7) desolve('diff(y(x),x)+x*y(x),y(x));
> d
> ----- (LAPLACE(y(x), x, LVAR)) + y(0)
> dLVAR
> (D7) y(x) = ILT(-------------------------------------, LVAR, x)
> LVAR
In cases like this, I would think that Maxima should respond more
gracefully. ode2 returns FALSE when it can't solve an ode; it seems
to me that other CASs will simply return the equation unsolved.
Which should be the proper behavior?
> as is to be expected. But have a look at describe(desolve), I think it's an
> unfair description at least.
It even claims to return FALSE when it fails, which it doesn't do (or
even try to do, as far as I can see in the code).
Jay