Mathematics

Problem

Consider the differential equation

\dfrac{dy}{dx}=x+y

. A portion of its slope field shows the following: • At

(0,1)

the small segment has slope

1

. • At

(0.1,1.1)

the small segment has slope

1.2

. Each segment extends

0.1

unit in the positive

x

-direction. What is the best estimate of

y

when

x=0.2

for the solution passing through

(0,1)

? a)

1.26

1.24

1.22

1.20