Which of the following expressions gives

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

Problem

y(x)

, the particular solution to the differential equation

\dfrac{dy}{dx}=\cos x

that satisfies

y(0)=2

? (a)

y(x)=2-\displaystyle\int_{0}^{x}\cos t\,dt

(b)

y(x)=2+\displaystyle\int_{0}^{x}\cos t\,dt

(c)

y(x)=\displaystyle\int_{0}^{x}\cos t\,dt

(d)

y(x)=2\cos x