Question: Consider the initial value problem dy dx =1+2xy, y(0)=0. Use the method of successive approximations (with 0(x)=0) to generate a sequence of functions {0(x),1(x),2(x),...,n(x)} for

Consider the initial value problem dy dx =1+2xy, y(0)=0. Use the method of successive approximations (with 0(x)=0) to generate a sequence of functions {0(x),1(x),2(x),...,n(x)} for an arbitrary value of n in N. Your answer should ultimately provide a formula for n(x), verified using induction. Show all working.

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