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function [t, w] = euler( f,a,b,N,alpha )
%[ w] = euler( f,a,b,N,alpha )
%INPUTS
% f -- function f(t,x)
% a -- begin point interval
% b -- end point interval
% N -- number of steps
% alpha -- initial condition x(a)
%OUTPUTS
% t -- the vector of times t_i
% w -- the vector of solutions at the times t_i

h=(b-a)/N;
w(1)=alpha;
for i=1:N+1;
    t(i)=a+(i-1)*h;
end
for i=1:N
    w(i+1)=w(i)+h*f(t(i),w(i));
end

return;...

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