April 23, 2013Prelim 3 V3Math 1106Please show your reasoning and all your work.This is a 90 minuteexam. Calculators are not needed or permitted. Good luck!Unless specifically requested, answers on this exam NEED NOTbe simplified or completely numerical. Arithmetic expressions arefine. Ordinarily, answers likeln125,3x2(x4-1)-4x3(x3+ 1)(x4-1)2,12(4x3)(x4+ 1).5are completely acceptable.Formula SheetPlease do not rip this sheet from your exam, as it will cause your exam tofall apart.Quadratic Formular=-b±√b2-4ac2awill give us the solution to the quadratic equationar2+br+c= 0.Integrating FactorFory0+P(x)y=Q(x)iseRP(x)dx.Problem 1) (16 Points)1a)Use separation of variables to find the general solution of the differentialequationdxdt=4t33x2.1