MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Consider the differential equation dxdy=y−x. Focus on the lattice of integer points satisfying −2≤x≤2 and −2≤y≤2.
(a) For each of the 25 lattice points in this domain, calculate the value of dxdy. Organize your work so the slopes corresponding to adjacent points can be compared easily.
(b) Using the slopes you computed, sketch a slope field on axes that include the given lattice. Draw a short line segment of appropriate inclination at every lattice point.
(c) Determine all straight lines in the plane along which every slope segment is identical. Explain how you located these lines and provide their equations.