Mathematics

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}

6+\dfrac{\pi}{2}

5+\dfrac{\pi}{2}

3+\dfrac{\pi}{2}