Please write in MAPLE Code to draw the direction field and solutions is given below (with explanatory comments)

Problem 1.

A. Have Maple produce a direction field for the differential equation y' = x(y-1)+y^2 for x and y in suitable intervals about zero. (Note: in entering the right hand side you must type x*(y(x)-1)+y(x)^2 ; juxtaposition of characters will not be interpreted as multiplication, and it must be explicitly indicated that y is a function of x.)

B. Now have Maple superimpose on the direction field the solutions that satisfy y(-1) = 0 and y(0) = 1 .

Problem 2.

We cannot solve the initial value problem y' = 1 - cos(xy), y(0) = 1 exactly. A. Create a direction field using Maple, and use it to describe the behavior of the solution. (See the note to 1(a) above.) B. Using the phaseportrait command, and adjusting the x and y intervals appropriately, estimate the value of x at which the solution assumes the value y = 2 . (Note that the initial point does not have to be in the window that you print and observe.)

Problem 3. A. For the o.d.e. y' = yx / (x^2 + 1) , predict the behavior of solutions as x increases without bound. Does the behavior depend on y? If so, describe how.