ExpressionSpaceODESolver(R, F)¶

Taylor series solutions of explicit ODE`'s`.

seriesSolve: (Equation F, BasicOperator, Equation F, Equation F) -> Any

`seriesSolve(eq, y, x=a, y a = b)` returns a Taylor series solution of `eq` around `x` = a with initial condition `y(a) = b`. Note: `eq` must be of the form `f(x, y x) y'(x) + g(x, y x) = h(x, y x)`.

seriesSolve: (Equation F, BasicOperator, Equation F, F) -> Any

`seriesSolve(eq, y, x=a, b)` is equivalent to `seriesSolve(eq, y, x=a, y a = b)`.

seriesSolve: (Equation F, BasicOperator, Equation F, List F) -> Any

`seriesSolve(eq, y, x=a, [b0, ..., b(n-1)])` returns a Taylor series solution of `eq` around `x = a` with initial conditions `y(a) = b0`, `y'(a) = b1`, `y''(a) = b2`, …, `y(n-1)(a) = b(n-1)` `eq` must be of the form `f(x, y x, y'(x), ..., y(n-1)(x)) y(n)(x) + g(x, y x, y'(x), ..., y(n-1)(x)) = h(x, y x, y'(x), ..., y(n-1)(x))`.

seriesSolve: (F, BasicOperator, Equation F, Equation F) -> Any

`seriesSolve(eq, y, x = a, y a = b)` is equivalent to `seriesSolve(eq=0, y, x=a, y a = b)`.

seriesSolve: (F, BasicOperator, Equation F, F) -> Any

`seriesSolve(eq, y, x = a, b)` is equivalent to `seriesSolve(eq = 0, y, x = a, y a = b)`.

seriesSolve: (F, BasicOperator, Equation F, List F) -> Any

`seriesSolve(eq, y, x = a, [b0, ..., bn])` is equivalent to `seriesSolve(eq = 0, y, x = a, [b0, ..., b(n-1)])`.

seriesSolve: (List Equation F, List BasicOperator, Equation F, List Equation F) -> Any

`seriesSolve([eq1, ..., eqn], [y1, ..., yn], x = a, [y1 a = b1, ..., yn a = bn])` returns a taylor series solution of `[eq1, ..., eqn]` around `x = a` with initial conditions `yi(a) = bi`. Note: eqi must be of the form `fi(x, y1 x, y2 x, ..., yn x) y1'(x) + gi(x, y1 x, y2 x, ..., yn x) = h(x, y1 x, y2 x, ..., yn x)`.

seriesSolve: (List Equation F, List BasicOperator, Equation F, List F) -> Any

`seriesSolve([eq1, ..., eqn], [y1, ..., yn], x=a, [b1, ..., bn])` is equivalent to `seriesSolve([eq1, ..., eqn], [y1, ..., yn], x = a, [y1 a = b1, ..., yn a = bn])`.

seriesSolve: (List F, List BasicOperator, Equation F, List Equation F) -> Any

`seriesSolve([eq1, ..., eqn], [y1, ..., yn], x = a, [y1 a = b1, ..., yn a = bn])` is equivalent to `seriesSolve([eq1=0, ..., eqn=0], [y1, ..., yn], x = a, [y1 a = b1, ..., yn a = bn])`.

seriesSolve: (List F, List BasicOperator, Equation F, List F) -> Any

`seriesSolve([eq1, ..., eqn], [y1, ..., yn], x=a, [b1, ..., bn])` is equivalent to `seriesSolve([eq1=0, ..., eqn=0], [y1, ..., yn], x=a, [b1, ..., bn])`.