# 11.3 Numerical Solutions # Art Belmonte, Summer 1996 # These are the shaded gray examples which appear in Section 11.3. # Here dsolve returns NULL, signifying that no solution could be found. > restart; eq3:=diff(y(t), t) + sin(y(t)^2) = 1; > dsolve({eq3, y(0)=1}, y(t)); /d \ 2 eq3 := |-- y(t)| + sin(y(t) ) = 1 \dt / > dsolve({eq3, y(0)=1}, y(t), numeric); proc(rkf45_x) ... end > f:=dsolve({eq3, y(0)=1}, y(t), numeric); f := proc(rkf45_x) ... end > f(0); f(0.5); [t = 0, y(t) = 1.] [t = .5, y(t) = 1.062032329712917] > with(plots): odeplot(f, [t, y(t)], 0..4); >