1. Write the following differential equations for the unknown function, y(z) with the variable z, in the standard form and illustrate the direction field by drawing the tangent intervals at the four points: (1,0), (0,1), (1,0) and (0, 1) in the (z, y)-plane. For each differential equation, find the general solution, then find the particular solution satisfying y(0) = 1, finally sketch the solution curve in the above illustration of direction field. All drawing and sketch must be done manually by hand. (2) (b)