A slope field is described as follows: • For every point whose x-coordinate is c
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A slope field is described as follows:
• For every point whose x-coordinate is c, the slope of the segment at that point equals c.
• Examples: At all points with x = −2 the slope is −2; at all points with x = 0 the slope is 0; at all points with x = 1 the slope is 1.
Four candidate differential equations are proposed:
(a) Determine which candidate differential equation is consistent with the slope field. State its roman numeral.
(b) Justify your choice by referring to specific features of the slope field description.
(c) For the differential equation you selected, find the general solution y(x).
(d) Determine the particular solution that passes through the point (0, 3).