radicalSolutions

**Usage**

radicalSolutions L

radicalSolutions(L,m)

Parameter |
Type |
Description |
---|---|---|

L |
A differential operator | |

m |
A positive integer |

**Returns**

Returns a matrix

such that the radical solutions ofLare described by

where and the are arbitrary constants. If a second argument is present, then only the solutions such that are returned.

**Remarks**

radicalSolutions returns only the solutions that are radical over ,i.e.the solutions such that for some integer . It does not return any eventual solution that is radical over but not over .

**Example**

We compute the radical solutions of

as follows:

1 --> L := 16*D^2 + 3/x^2; 2 --> r := radicalSolutions(L); 3 --> tex(r);

This means that the radical solutions of (7) form a two-dimensional vector space over the constants generated by and .

**Usage within MAPLE **

- When using radicalSolutions from inside MAPLE, the result
returned from BERNINA is transformed into actual radicals,
so the above example in MAPLE would be:
> L := 16*D^2 + 3/x^2; > radicalSolutions(L, D, x);

**See Also**`exponentialSolutions`