generate the plot of the Newton polygon of a linear differential operator at a point
DEplot_polygon(L, y, (x = x0))
linear homogeneous differential equation
unknown function to search for
(optional) irreducible polynomial or infinity
The DEplot_polygon function computes a plot of the Newton polygon of a linear differential operator at the point x0. The linear differential operator L corresponds to the differential equation L⁡y=0.
The equation L⁡y=0 must be homogeneous and linear in y and its derivatives, and its coefficients must be rational functions in the dependent variable x.
x0 must be a rational or an algebraic number or the symbol infinity. If x0 is not passed as an argument, x0 = 0 is assumed.
This function is part of the DEtools package, and so it can be used in the form DEplot_polygon(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[DEplot_polygon](..).
ode ≔ ⅆ4ⅆx4⁢y⁡x⁢x7−ⅆⅆx⁢y⁡x⁢x+x7−y⁡x⁢x9
The command to create the plot from the Plotting Guide is
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