Define the function that describes the ODE. Use the code "f:=(x,y)->function;", where "function is the specific function of the ODE. For example, if you want to use Euler's method to solve the ODE "dy/dx = x + y;", you should type "f:=(x,y)->x+y;".
Set up the initial conditions of the ODE. The initial conditions that accompany the ODE are given in the form "y(a)=b;". In Maple, define these initial conditions by setting "x" equal to "a" and "y" equal to "b". The code is "x:=a;" and "y:=b;". For example, if the initial conditions are "y(0)=1" then you would type "x:=0;" and "y:=1;".
Choose the increment for Euler's method. The increment for Euler's method affects the speed at which the method arrives at a solution. In practice, your choice of the increment is arbitrary and rather unimportant. Common choices are numbers between 0 and .5. If you have no preference, choose something low, such as 0.1. The Maple code for setting the increment is "h:=increment;". For example, "h:=0.1;".
Create a place to store the solution. Since the solution will be a sequence of numerical values that represent x and y, store them in sets. Use the code "soln:=[x,y];".
Run Euler's method through a do loop. Create the following loop: "F:=f(x,y); x:=x+h; y:=y+h*F; soln:=soln,[x,y]; od:" This will run Euler's method on the ODE. The solution is stored in "soln".