A solution curve for the differential equation passes through

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A solution curve for the differential equation

\dfrac{dy}{dx}=y(2-x)

passes through

(1,2)

. The slope field indicates that • at

(1,2)

the slope is

2

, and • at

(1.5,3)

the slope is

1.5

. If each small segment is

0.5

unit long in the

x

-direction, which of the following is the best estimate of

y

when

x=2

? (a) 3.50 (b) 3.75 (c) 4.00 (d) 3.00