A function satisfies with

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

A function

y(x)

satisfies

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

with

y(0)=1

. Starting at

(0,1)

, one straight-line step of length

h=0.2

is taken to approximate

y(0.2)

. The exact value at

x=0.2

1.2428

(rounded to four decimal places). Determine the absolute error of the approximation, rounded to three decimal places.