function y = Euler_step_method( final_time, N_steps )
%runs an Euler step method for solving an ODE
%from time t=0 to t=final_time
%solves y' = t^2 +y^2, y(t=0)=1

y(1) = 1;
t(1) = 0;

dt = (final_time - t(1)) / N_steps;

for i=1:1:N_steps
    t(i+1) = t(i) + dt;
    y(i+1) =  y(i) + (t(i)^2 + y(i)^2 ) * dt;
    
end

plot(t,y)