Mathematics

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

4.5

3.8

4.0