restart: with(plots):with(DEtools):f:=(t,x) -> 2*t*x + exp(t^2);DE:=diff(v(t),t)=2*t*v(t)+exp(t^2);dsolve(DE,v(t));plot2:=DEplot(DE,v(t),t=-1..1.5,v=-1..20,[[v(0)=1]]):t0:= 0: x0:= 1:h:= 0.1:n:= 15:t:= t0: x:= x0:for i from 1 to n do x:= x+h*f(t,x): t:= t+h: print(t,x); P[i]:=[t,x]; od:plot1:=plot([seq(P[i],i=1..n)],style=point,color=green):display(plot1,plot2);f1:= (t,x,y,z)->t*x-y+z;f2:= (t,x,y,z)->3*x+y-z;f3:= (t,x,y,z)->x+y-t*z;t0:=0: x0:=1: y0:=1: z0:=0:h:= 0.1:n:= 15:t:=t0: x:=x0: y:=y0: z:=z0:for i from 1 to n do u:=f1(t,x,y,z): v:=f2(t,x,y,z): w:=f3(t,x,y,z): x:=x+h*u: y:=y+h*v: z:=z+h*w: t:=t+h: print(t,x,y,z);od: