Math 3301Homework Set 110 PointsSketch the direction field for each of the following differential equations. Based on your direction field sketch determine the behavior of the solution, Basics( )yt, as t→∞(i.e.the long term behavior). If this behavior depends upon the value of ( )0ygive this dependence. 1. ( ) ( )( )24224dyyyydt=+−−2.( )( )3221y−′=−+eFor problems 3 & 4 solve the given IVP. Linear Differential Equations3.( ) ( ) ( )222322204xxyxyxy−′+=++=e4. ( ) ( )4437632310ttytt y ty′− +=−=e5.It is known that the solution to the following differential equation will have a relative maximum at 12t=. Assuming that the solution and its derivative exist and are continuous for all tdetermine the value of the solution at this point (i.e.find ( )12y). Note that because you don’t have an initial condition you can’t actually solve this differential equation. It is still possible however to answer this question. 643t′+=−eHint : Recall from Calc I where relative extrema may occur and don’t forget the differential equation,
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