For the differential equation with

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

Problem

For the differential equation

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

with

y(0)=2

, a student uses Euler’s method with a constant step size of

\Delta x = 0.5

to approximate

y(3)

. Which of the following values is closest to the student’s estimate after six steps? (a)

5.2

(b)

4.5

(c)

3.8

(d)

4.0