y(0) = 0 Problem 3 dy = 1 – x + x? Consider the initial value problem dx ,0

Please solve (e) part only

Extracted text: y(0) = 0 Problem 3 dy = 1 – x + x? Consider the initial value problem dx ,0 < x="">< 2.="" (a)="" find="" the="" analytic="" solution="" to="" this="" ivp="" by="" integration.="" (b)="" use="" the="" forward="" euler="" algorithm="" to="" numerically="" estimate="" the="" true="" solution="" at="" x="2," using="" 4="" panels="" of="" equal="" width.="" (c)="" use="" the="" forward="" euler="" algorithm="" to="" numerically="" estimate="" the="" true="" solution="" at="" x="2," using="" n="" panels="" of="" equal="" width,="" where="" n="" en="" is="" arbitrary.="" your="" estimate="" for="" y(2),="" namely="" yn,="" should="" depend="" on="" n.="" (d)="" show="" that="" for="" your="" estimates="" from="" part="" (c),="" it="" is="" the="" case="" that="" lim="" yn="y(2)" (e)="" let="" x*="" forward="" euler="" with="" n="" steps="" causes="" our="" numerical="" estimate="" for="" y(x*)="" to="" approach="" the="j/2m" for="" some="" m="" e="" n="" and="" some="" je="" {0,="" 1,="" ...,="" 2m+1}.="" show="" that="" using="" true="" solution="" in="" the="" limit="" as="" n="" →="">