The function satisfies with the initial condition

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The function

y

satisfies

\dfrac{dy}{dx}=x\sin(x^{2})

with the initial condition

y(0)=2

. Which of the following gives an explicit formula for

y(x)

? (a)

y(x)=3-\cos\left(x^{2}\right)

(b)

y(x)=\dfrac{5}{2}-\dfrac{1}{2}\cos\left(x^{2}\right)

(c)

y(x)=\dfrac{3}{2}+\dfrac{1}{2}\cos\left(x^{2}\right)

(d)

y(x)=2-\dfrac{1}{2}\cos\left(x^{2}\right)