This program has only 6 lines of input. It is written according to the instructions in our textbook page 418.
Input your function. Please use := here

f[t_, y_] :=  t^2  +  y^2

Input initial data, mesh size, and total number of steps.

t = 0;  y = 0; h = 0.01; n = 100;

Find initial pair of values:

sol = {{t, y}}

The loop for finding all other pairs using Euler method, and appended to the solution table "sol":

\(For[j = 0, j < n, \(j++\), 

      	{k1 = f[t, h], y = y + h*k1, t = t + h, \ sol = Append[sol, {t, y}]}]
      \)

Plot the solution table "sol", and joint the points by lines.

ListPlot[sol, PlotJoined -> True]

If you want to look at your data set for your solution in terms of (t,y) pairs, do this:

sol