For the differential equation with the initial condition

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

For the differential equation

\dfrac{dy}{dx}=\sin x+1

with the initial condition

y(0)=4

, determine the exact value of

y\!\left(\dfrac{\pi}{2}\right)

. (a)

4+\dfrac{\pi}{2}

(b)

6+\dfrac{\pi}{2}

(c)

5+\dfrac{\pi}{2}

(d)

3+\dfrac{\pi}{2}