MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Consider the differential equation dxdy=3x2. Three candidate expressions are proposed as solutions:
(a) Identify which of the three expressions represents the general solution of the differential equation and which represent particular solutions. State your choices clearly.
(b) For each expression you classified as a particular solution, verify algebraically that it satisfies the differential equation. Show all steps.
(c) Describe, in words, how the family of curves given by the general solution differs graphically from each of the particular solutions when sketched on the same slope field.