exponentialSolutions

**Usage**

exponentialSolutions L

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

L |
A differential operator |

**Returns**

Returns such that the exponential solutions ofLare described by

where and the are arbitrary constants.

**Remarks**

exponentialSolutions returns only the solutions that are exponential over ,i.e.the solutions such that . It does not return any eventual solution that is exponential over but not over .

**Example**

We compute the exponential solutions of

as follows:

1 --> L := D^3-(1+x^3)/x*D^2+(-3*x-2*x^2)*D+2*x^4; 2 --> e := exponentialSolutions(L); 3 --> tex(e);

This means that the exponential solutions of (4) form a one-dimensional vector space generated by .

**Usage within MAPLE **

- When using exponentialSolutions from inside MAPLE, the result
returned from BERNINA is transformed into actual exponentials,
so the above example in MAPLE would be:
> L := D^3-(1+x^3)/x*D^2+(-3*x-2*x^2)*D+2*x^4; > exponentialSolutions(L, D, x);

**See Also**`radicalSolutions`