# UnivariateTaylorSeriesODESolver(Coef, UTS)ΒΆ

- Coef: Algebra Fraction Integer
- UTS: UnivariateTaylorSeriesCategory Coef

This package provides Taylor series solutions to regular linear or non-linear ordinary differential equations of arbitrary order.

- fixedPointExquo: (UTS, UTS) -> UTS
`fixedPointExquo(f, g)`

computes the exact quotient of`f`

and`g`

using a fixed point computation.

- mpsode: (List Coef, List List UTS -> UTS) -> List UTS
`mpsode(r, f)`

solves the system of differential equations`dy[i]/dx =f[i] [x, y[1], y[2], ..., y[n]]`

,`y[i](a) = r[i]`

for`i`

in 1..`n`

.

- ode1: (UTS -> UTS, Coef) -> UTS
`ode1(f, c)`

is the solution to`y' = f(y)`

such that`y(a) = c`

.

- ode2: ((UTS, UTS) -> UTS, Coef, Coef) -> UTS
`ode2(f, c0, c1)`

is the solution to`y'' = f(y, y')`

such that`y(a) = c0`

and`y'(a) = c1`

.

- ode: (List UTS -> UTS, List Coef) -> UTS
`ode(f, cl)`

is the solution to`y<n>=f(y, y', .., y<n-1>)`

such that`y<i>(a) = cl.(i+1)`

for`i`

in 0..(`n`

- 1).

- stFunc1: UTS -> UTS -> Stream Coef -> Stream Coef
`stFunc1(f)`

is a local function exported due to compiler problem. This function is of no interest to the top-level user.