A student applies Euler’s Method with step size to the differential equation

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

Problem

A student applies Euler’s Method with step size

\Delta x=0.5

to the differential equation

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

, starting at

(0,1)

, and obtains the estimate

y(1)=0.25

. Determine whether this estimate is an overestimate or an underestimate of the actual value of

y(1)

, and justify your answer.