gfun[guessode] - guess a nonlinear differential equation for a power series
Calling Sequence
guessode(s, y(x), options)
Parameters
s - a power series expanded at 0
y(x) - the unknown function and the series variable
options - optional equations controlling the search
Description
- The
guessodecommand searches for a nonlinear differential equation with polynomial coefficients satisfied by the power seriess. - The command returns a set containing the guessed equation and the initial conditions required to identify the series solution, or
FAILif no equation is found within the requested bounds. - The options
minordereqn,maxordereqn,maxdegcoeffs,totaldegree,maxdegree,checkterms,mode, andmodulocontrol the search. The optionmaxdegreeis accepted as an alias fortotaldegree. For more information on the common gfun search options, see gfun[parameters]. - This command is part of the
gfunpackage, so it can be used in the formguessode(..)after executingwith(gfun). It can always be accessed throughgfun[guessode](..).
Examples
> with(gfun):> s := series(tan(x), x, 12):> guessode(s, y(x));\[\{2 \frac{d^{2}}{d x^{2}}y \! \left(x \right)-3 \left(\frac{d}{d x}y \! \left(x \right)\right) \left(\frac{d^{2}}{d x^{2}}y \! \left(x \right)\right)+y \! \left(x \right) \left(\frac{d^{3}}{d x^{3}}y \! \left(x \right)\right), y \! \left(0\right) = 0, D\! \left(y \right)\! \left(0\right) = 1, D^{\left(2\right)}\! \left(y \right)\! \left(0\right) = 0\}\]
See Also
gfun, gfun[guessrelation], gfun[hermite_pade], gfun[listtodiffeq], gfun[parameters]