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(Solved): (c) Following the result in (b), an alternative way of defining "Picard's iterates" would be to set ...
(c) Following the result in (b), an alternative way of defining "Picard's iterates" would be to
set y-=1 and
y_(n+1)(x)=e^(x)(1+\int_0^x e^(-t)f(t,y_(n)(t))dt)
For the IVP:
(dy)/(dx)=y+y^(2),y(0)=1
compute the first 3 of (the standart) picards iterates and the first 3 of the alternative iterates