1. Consider IVT problem: y'-1.5y=3t+2et, y(0)= y0 Find y0 value that seperates solutions that grow positively as t->∞ from those that grow negatively. How does the soln that corresponds to this critical value or y0 behave as t->∞? 2. Basically i'm drawing a direction field first, but how am i supposed to see the graph of the functions y(not)=-3, -2 ,-1 ,0 etc..... to see the behaviour as t->∞ if the function is so complicated. i've solved the differential equation it's: -(24/37)cos(3t)-(4/37)sin(3t)+(y0+24/37)et/2 if we could use graphing calculators i could just plug it in and see the behaviour for values of y(not), but there's no calculators allowed on the test 3. I solved the differential equations but i have to idea how to graph this to view the behaviours. Is this what i'm supposed to do? Or is there an easier way to see this that i don't know about i'm stuck i have the solution but i don't know what y0 has to do with the behaviour of the DE. And how i determine what y0 values do the DE.