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### exponentialSolutions

Usage

exponentialSolutions L

Parameter Type Description
L A differential operator

Returns

Returns such that the exponential solutions of L are 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

 (4)

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);

Next: exteriorPower Up: Supported functions Previous: element   Contents   Index
Manuel Bronstein 2002-09-04