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shuping (wrs829) – HW9 – perutz – (52760)3After separating variables and integrating,the given differential equation becomes-integraldisplay1y2dy=1y=integraldisplay3 lnx dx.To integrate the right hand side we integrateby parts. Thus1y= 3(xlnx-x) +CwithCan arbitrary constant. Fory1the valueofCis determined by the conditiony(1) =18sincey(1) =18=⇒C= 11.Consequently,y1(x) =13(xlnx-x) + 11.Atx=e, therefore,y1(e) =111.00510.0pointsNewton’s Law of Cooling asserts that therate of change of temperature of an object