# ODETools(F, LODO)ΒΆ

- F: Field
- LODO: LinearOrdinaryDifferentialOperatorCategory F

`ODETools`

provides tools for the linear ODE solver.

- particularSolution: (LODO, F, List F, F -> F) -> Union(F, failed)
`particularSolution(op, g, [f1, ..., fm], I)`

returns a particular solution`h`

of the equation`op y = g`

where`[f1, ..., fm]`

are linearly independent and`op(fi)=0`

. The value “failed” is returned if no particular solution is found. Note: the method of variations of parameters is used.

- variationOfParameters: (LODO, F, List F) -> Union(Vector F, failed)
`variationOfParameters(op, g, [f1, ..., fm])`

returns`[u1, ..., um]`

such that a particular solution of the equation`op y = g`

is`f1 int(u1) + ... + fm int(um)`

where`[f1, ..., fm]`

are linearly independent and`op(fi)=0`

. The value “failed” is returned if`m < n`

and no particular solution is found.

- wronskianMatrix: (List F, NonNegativeInteger) -> Matrix F
`wronskianMatrix([f1, ..., fn], q, D)`

returns the`q x n`

matrix`m`

whose i^th row is`[f1^(i-1), ..., fn^(i-1)]`

.