A routine approximates the solution to with using a variable increment rule: • Start with

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

Problem

A routine approximates the solution to

y'=x+y^{2}

with

y(0)=0

using a variable increment rule: • Start with

h_1=0.20

. • After each accepted step, set the next increment

h_{k+1}=0.9h_k

|f(x_k,y_k)|>1

, and

h_{k+1}=1.1h_k

otherwise, subject to

0.05\le h_{k+1}\le0.30

. After two accepted steps the program reaches

x_2=0.42

with

y_2\approx0.044

. Which value will the program use for the third increment

h_3

? (a)

0.18

(b)

0.30

(c)

0.24

(d)

0.22