Consider the differential equation with initial condition

MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations

Problem

Consider the differential equation

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

with initial condition

y(0)=1

. Let

y_{\text{E}}(0.4)

be the approximation obtained using a uniform step size of

h=0.2

. The exact solution is

y(x)=-x-1+2e^{x}

. What is the absolute error

\bigl|y_{\text{E}}(0.4)-y(0.4)\bigr|

? (a)

0.066

(b)

0.184

(c)

0.104

(d)

0.016