If $\frac{dy}{dx} = y\cos x$ and $y = 1$ when $x = 0$, what is $y$ when $x = \frac{\pi}{2}$?

Explanation

1. 01

   Separating and integrating gives the general solution; the condition $y(0) = 1$ fixes the constant.

2. 02

   The particular solution is $y = e^{\sin x}$.

3. 03

   At $x = \frac{\pi}{2}$: $y = e$.