please solve all parts of differential equation and show work. thank you!

5. The logistic equation for the population (in thousands) of a certain species is given by dtdp=3p2p2. (a) Sketch the direction field by using either a computer software package or the method of isoclines. (b) Argue that the graph of is decreasing for x near zero and that as x increases from zero, (x) decreases until it crosses the line y=x, where its derivative is zero. (c) Let x be the abscissa of the point where the solution curve y=(x) crosses the line y=x. Consider the sign of (x) and argue that has a relative minimum at x. (d) What can you say about the graph of y=(x) for x>x ? (e) Verify that y=x1 is a solution to dy/dx=xy and explain why the graph of (x) always stays above the line y=x1. (f) Sketch the direction field for dy/dx=xy by using the method of isoclines or a computer software package. (g) Sketch the solution y=(x) using the direction field in part (f)