Given with , use three successive steps of sizes , , and to obtain a numerical…

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

Problem

Given

\dfrac{dy}{dx}=x^{2}-y

with

y(0)=2

, use three successive steps of sizes

h_1=0.05

h_2=0.10

, and

h_3=0.05

to obtain a numerical approximation for

y(0.20)

. Report your answer rounded to three decimal places.