3.46 How to plot solution to first order using Improved Euler numerical method?

This is done using Student:-NumericalAnalysis:-InitialValueProblem as follows. Note this is called heun method in Maple.

ode:=diff(y(x),x)=2*x*y(x)+x; 
IC:=y(0)=1; 
ending_x:=2; 
Student:-NumericalAnalysis:-InitialValueProblem(ode,IC, 
          x=ending_x,'method'='rungekutta','submethod'='heun', 
          'numsteps'=41,'output'='plot','plotoptions'=['gridlines']);
 

To obtain table of values instead do this

ode:=diff(y(x),x)=2*x*y(x)+x; 
IC:=y(0)=1; 
ending_x:=2; 
Student:-NumericalAnalysis:-InitialValueProblem(ode,IC, 
          x=ending_x,'method'='rungekutta','submethod'='heun', 
          'numsteps'=41,'output'='information');