Learning Guide Learning Guide

6.2 Ordinary Differential Equations • 243[1 − x + 1 6 x2 − 190 x3 + 1 12520 x4 −113400 x5 ,%1 + 1 − x + 1 6 x2 − 190 x3 + 1 12520 x4 −113400 x5 ,2 %1 + 1 − x + 1 6 x2 − 190 x3 + 1 12520 x4 −113400 x5 ,3 %1 + 1 − x + 1 6 x2 − 190 x3 + 1 12520 x4 −113400 x5 ,4 %1 + 1 − x + 1 6 x2 − 190 x3 + 1 12520 x4 −113400 x5 ,5 %1 + 1 − x + 1 6 x2 − 190 x3 + 1 12520 x4 −113400 x5 ]%1 :=√ 1 x (1 −3 x + 130 x2 − 1630 x3 + 122680 x4 −> plot( %, x=1..10 );11247400 x5 )3210–1–2–3–42 4x6 8 10The type=numeric Option Although the series methods for solvingODEs are well understood and adequate for finding accurate approximationsof the dependent variable, they do exhibit some limitations. Toobtain a result, the resultant series must converge. Moreover, in the processof finding the solution, Maple must calculate many derivatives, whichcan be expensive in terms of time and memory. For these and other reasons,alternative numerical solvers have been developed.Here is a differential equation and an initial condition.> eq := x(t) * diff(x(t), t) = t^2;eq := x(t) ( d x(t)) = t2dt> ini := x(1) = 2;