ReductionOfOrder(F, L)

odeef.spad line 502 [edit on github]

• F : Field
• L : LinearOrdinaryDifferentialOperatorCategory(F)

ReductionOfOrder provides functions for reducing the order of linear ordinary differential equations once some solutions are known.

ReduceOrder : (L, F) -> L

ReduceOrder(op, s) returns op1 such that for any solution z of op1 z = 0, y = s \int z is a solution of op y = 0. s must satisfy op s = 0.

ReduceOrder : (L, List(F)) -> Record(eq : L, op : List(F))

ReduceOrder(op, [f1, ..., fk]) returns [op1, [g1, ..., gk]] such that for any solution z of op1 z = 0, y = gk \int(g_k-1 \int(... \int(g1 \int z)...)) is a solution of op y = 0. Each fi must satisfy op fi = 0.