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Topic: a CAS program that shows step-by-step solution to simple ODE's
Replies: 18   Last Post: Aug 15, 2017 6:09 PM

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 clicliclic@freenet.de Posts: 1,245 Registered: 4/26/08
Re: a CAS program that shows step-by-step solution to simple ODE's
Posted: Aug 13, 2017 12:31 PM

"Nasser M. Abbasi" schrieb:
>
> On 8/12/2017 12:50 PM, clicliclic@freenet.de wrote:
>

> >> It currently handles 1st order: linear, separable,
> >> exact, Bernoulli, Riccati [...]
> >>

> >
> > The general-purpose procedure DSOLVE1() in the library file
> > FirstOrderODEs.mth shipped with Derive 6.10 is claimed to solve
> > exact, linear, separable, homogenous and generalized homogenous
> > differential equations, as well as equations possessing an
> > integrating factor that depends only on x or only on y. There is
> > also a separate test for an integrating factor of the form x^m*y^m.
> >
> > For Bernoulli and other special ODEs (among them Clairaut) there are
> > dedicated procedures.
> >

>
> Thanks for the info. I do not have or use Derive. But
> does it show step-by-step solution, as one does by hand?
> That would be interesting if it does.
>
> My program solves non-exact first order ODE's which
> can be made exact using integrating factor showing all the
> steps. Here is one such problem
>
> http://12000.org/my_notes/solving_ODE/inse12.htm#x15-2940002.5.17
>

This is your test problem 21: y + (2*x - y*exp(y))*y' = 0 which Derive
6.10 also solves right away:

DSOLVE1(y, 2*x - y*EXP(y), x, y, x0, y0)

#e^y*(y^2 - 2*y + 2) - #e^y0*(y0^2 - 2*y0 + 2) - x*y^2 + x0*y0^2 = 0

Executing this step-wise, however, one gets bogged down into step-wise
differentiation when the solution strategy is determined. It is much
easier to examine the code in FirstOrderODEs.mth.

Another class are homogeneous and generalized homogeneous equations, the
latter when written as y' = r(x, y) requiring

x/y*DIF(x/y*r(x, y), x)/DIF(x/y*r(x, y), y)

to depend neither on x nor on y. The equation can then be handled as a
separable one.

Martin.

Date Subject Author
8/11/17 Nasser Abbasi
8/11/17 bursejan@gmail.com
8/12/17 clicliclic@freenet.de
8/12/17 Nasser Abbasi
8/13/17 clicliclic@freenet.de
8/13/17 Nasser Abbasi
8/13/17 Nasser Abbasi
8/13/17 drhuang57@gmail.com
8/14/17 Nasser Abbasi
8/14/17 drhuang57@gmail.com
8/14/17 Nasser Abbasi
8/14/17 drhuang57@gmail.com
8/14/17 drhuang57@gmail.com
8/15/17 Richard Fateman
8/15/17 Bernice Barnett
8/15/17 bursejan@gmail.com
8/15/17 bursejan@gmail.com
8/15/17 Guest
8/15/17 Nasser Abbasi