Consider the differential equation with initial condition

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

Problem

Consider the differential equation

\dfrac{dy}{dx}=x+y

with initial condition

y(0)=1

. A single tangent-line step of size

h=0.2

is used to approximate

y(0.2)

. Determine whether the resulting numerical estimate is greater than or less than the actual value of

y(0.2)

for the solution of the differential equation.