Consider the differential equation dx/dy=-xy^2

a) Sketch a slope field for the given differential equation at the 15 points indicated.

b) Let y = f(x) be the particular solution to the differential equation with the initial condition f(-1) = 1. Write an equation for the line tangent to the graph of y = f(x) at x = -1. Use your equation to approximate f(-0.9).

c) Find the particular solution y = f(x) to the given differential equation with the initial condition f(-1) = 1.

No calculator is allowed for the following problem. Consider the differential equation dy = xy2. x a) On the axes provided, sketch a slope eld for the given differential equation at the 15 points indicated. b) Let y =x) be the particular solution to the differential equation with the initial condition 1) = 1. Write an equation for the line tangent to the graph of y =x) at x = 1. Use your equation to approximate 0.9). c) Find the particular solution y =x) to the given differential equation with the initial condition 1)=1