# === Example 1 === with(DEtools): de:=diff(x(t),t)=x(t)*(2-x(t)): var:=x(t):tDomain:=t=0..5: dots:=[[x(0)=1],[x(0)=1.5],[x(0)=2.2],[x(0)=-0.2]]: wind:=x=-2..3: opts:=linecolor=BLACK,thickness=3,stepsize=0.1: DEplot(de,var,tDomain,dots,wind,opts); # === Example 2 === # This plot can also be carried out from a GUI Tool in maple 12 to 18. # To find it, start java maple 12 to 18, then goto menu item # TOOLS ==> ASSISTANTS ==> ODE ANALYZER # An equivalent command in either a java or non-java worksheet is dsolve[interactive](); # Once started, enter the differential equation as ## diff(x(t),t)=x(t)*(2-x(t)) # and the initial condition as ## x(0)=1.5 # Try buttons ## SOLVE SYMBOLICALLY ### Click on SHOW MAPLE COMMANDS ## SOLVE ## PLOT # === Example 3 === with(DEtools): de:=diff(x(t),t)=x(t)*(1-x(t)): vars:=x(t): wind:=t=0..5,x=-0.2..3: ic:=[[x(0)=1.2],[x(0)=1],[x(0)=0],[x(0)=0.5]]: opts:=stepsize=.2,title=`Verhulst model`,arrows=MEDIUM: DEplot(de,vars,wind,ic,opts);