Mathematics

Problem

The differential equation

\frac{dy}{dx}=y

has exact solution

y=e^{x}

satisfying

y(0)=1

. (a) Using two equal horizontal steps of length

0.5

and the slopes given by the differential equation at the beginning of each step, estimate

y(1)

. Round to the nearest hundredth. (b) Compute the absolute error between your estimate in part (a) and the exact value

e^{1}

. Round to the nearest hundredth.