Consider the differential equation dy/dx = 1/3x(y-2)^2.
(a) A slope field for the given differential equation is shown below. Sketch the solution curve that passes through the point (0, 2), and sketch the solution curve that passes through the point (1, 0).
(b) Let y = f(x) be the particular solution to the given differential equation with initial condition f(1) = 0. Write an equation for the line tangent to the graph of y = f(x) at x = 1. Use your equation to approximate f(0.7).
(c) Find the particular solution y = f(x) to the given differential equation with initial condition f(1) = 0.
