It is instructive to see how Picard's method works with a choice of the initial approximation other than the constant function yo(x)=yo. Apply the method to the initial value problem (4) with (a) yo(x)=e^x; (b) yo(x)=1+x;
(c) yo(x) = cos x. And then, Plot the solutions. Irrespective of the chosen initial approximation, the Picard iterates seem to converge, why? Hint: For (C), approximate cos x by taking appropriate number of terms of its Taylor series.