Two slope fields

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Two slope fields, labeled A and B, have the following properties: • Field A: The slope is

0

along the line

y=0

, and when the

y

–coordinate doubles, the slope doubles; slopes are identical for all points with the same

y

‐value. • Field B: The slope is

0

along the line

x=0

, and when the

x

–coordinate triples, the slope triples; slopes are identical for all points with the same

x

‐value. Consider the differential equations (1)

\dfrac{dy}{dx}=2y

(2)

\dfrac{dy}{dx}=3x

. Match each field with its corresponding equation and report your answer in the form “A–__, B–__”.