Assignment:
Consider the differential equation (dy/dx) = (-xy^2)/2. Let y=f(x) be the particular solution to this differential equaiton with the initial condition f(-1)=2.
a) On the axis provided sketch a slope field for the given differential equation t the twelve points indicated. (the x-axis goes from -1 to 2 and the y-axis goes from 0 to 2).
b) Write an equation for the line tangent to the graph of f at x=-1.
c) Find the solution y=f(x) to the given differential equation with the initial condition f(-1)=2.
Provide complete and step by step solution for the question and show calculations and use formulas.