
Re: a CAS program that shows stepbystep 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 generalpurpose 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 stepbystep solution, as one does by hand? > That would be interesting if it does. > > My program solves nonexact 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#x152940002.5.17 >
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 stepwise, however, one gets bogged down into stepwise 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.

