Example 7

\begin{align*} y^{\prime } & =\sin y\\ y\left ( 0\right ) & =\pi \end{align*}

Since this is of form \(y^{\prime }=f\left ( y\right ) \) and IC is given then we check if \(y=\pi \) satisfies the ode itself or not. We see that \(0=\sin \left ( \pi \right ) =0\). Hence it does. Hence the solution is

\begin{align*} y & =y_{0}\\ & =\pi \end{align*}