The Slode package contains commands to find formal power series solutions of linear ordinary differential equations and determine points for some special series solutions (hypergeometric, rational, polynomial, and sparse series).

Each command in the Slode package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

The following is a list of available commands.

To display the help page for a particular Slode command, see Getting Help with a Command in a Package.

For information on the data structure used to represent an ODE, see LODEstruct.

For references about the algorithms implemented in the package, see Slode,references.

The Slode package example worksheet provides a brief overview of the package.

$L≔2x\left(x-1\right)\mathrm{diff}\left(\mathrm{diff}\left(y\left(x\right)\,x\right)\,x\right)+\left(7x-3\right)\mathrm{diff}\left(y\left(x\right)\,x\right)+2y\left(x\right)\:$

$\mathrm{Slode}:-\mathrm{candidate\_points}\left(L\,y\left(x\right)\right)$

$\left[\left\{0\,1\,\mathrm{any\_ordinary\_point}\right\}\,\left\{0\,1\right\}\,\left\{\mathrm{-1}\,0\right\}\right]$

$\mathrm{Slode}:-\mathrm{hypergeom\_series\_sol}\left(L\,y\left(x\right)\,1\right)$

$\frac{{\mathrm{\_C}}_0\left(\sum _{\mathrm{\_n}=0}^{\mathrm{\infty }}\frac{\mathrm{\Gamma }\left(\frac{1}{2}+\mathrm{\_n}\right){\left(\mathrm{-1}\right)}^{\mathrm{\_n}}{\left(x-1\right)}^{\mathrm{\_n}}}{\mathrm{\Gamma }\left(\mathrm{\_n}+1\right)}\right)}{\sqrt{\mathrm{\pi }}}$

$\mathrm{Slode}:-\mathrm{rational\_series\_sol}\left(L\,y\left(x\right)\,0\right)$

$2{\mathrm{\_C}}_1\left(\sum _{\mathrm{\_n}=0}^{\mathrm{\infty }}\frac{\left(\mathrm{\_n}+1\right)x^{\mathrm{\_n}}}{2\mathrm{\_n}+1}\right)$