MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Consider the differential equation
dxdy=x2−y.
Four slope-field descriptions, labelled A–D, are given.
(a) Indicate which description (A, B, C, or D) matches the given differential equation.
(b) Provide two separate mathematical reasons supporting your choice in part (a). Each reason must relate a specific feature of the differential equation to an observed feature in the matching description.
(c) Let the solution curve through the point (1, 1) be denoted by y = s(x). Using the differential equation, determine whether s(x) is increasing or decreasing at x = 1 and decide whether it is concave upward or concave downward there. Confirm that these conclusions are consistent with the slope-field description you selected.