Learning Guide Learning Guide

246 • Chapter 6: Examples from Calculus[t = 1., x(t) = 5.58216755967155986,y(t) = 7.82688931187210190]Use the odeplot command to plot y(t) against x(t),> odeplot( sol1, [x(t), y(t)], -3..1, labels=["x","y"] );86y420–22 3 4 5 6x–4x(t) and y(t) against t,> odeplot( sol1, [t, x(t), y(t)], -3..1,> labels=["t","x","y"], axes=boxed );y8–42–3x61tor any other combination.Always use caution when using numeric methods because errors canaccumulate in floating-point calculations. Universal rules for preventingthis effect do not exist, so no software package can anticipate all conditions.The solution is to use the startinit option to make dsolve (orrather the procedure which dsolve returns) begin at the initial value forevery calculation at a point (x, y(x)).You can specify which algorithm dsolve(..., type=numeric) useswhen solving your differential equation. Refer to ?dsolve,numeric.