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...Calculusiiassignmentsolutions findthegeneralsolutiontothefollowingdifferentialequations i y xy iv px ii dy ex v d tsec dx dt et iii dz z p vi t tz solutions theequationin isaseparableequation souponwriting andisolating variables we have xdx x c for an arbitrary constantc takingnegativereciprocals wehave asthesolutionto isalineardifferentialequationwithp thustheintegrating factor this equation is e r hence integratingbothsides thisgives so uponsolvingfor weget any asthegeneralsolutiontotheequationin rearrangingandisolatingthevariables zdz etdt takinglogarithmsonbothsides weseethatthegeneralsolutionof log isalineardifferentialequation upondividingthroughbyx wewillhave andq thustheintegratingfactorforthisequationis andthus uponmultiplyingthroughtheequationandintegrating thereforethegeneralsolutionto isseparable rearrangingandintegratingyields te tdt sec onthelefthandside cos sin ontherighthandside eudu puttingthingstogethergivestheequation thisgivesanimplicitequationfor finally another li...