For the differential equation with initial condition

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

Problem

For the differential equation

\dfrac{dy}{dx}=y

with initial condition

y(0)=1

, three equal straight-line steps of length

0.1

are taken to approximate

y(0.3)

. The approximate value obtained is

1.331

. The exact value is

e^{0.3}\approx1.3499

. Calculate the percentage error of the approximation, to the nearest hundredth of a percent.