4.2.2.2 Example

\begin{align*} y^{\prime \prime }+y & =\frac {1}{x}\\ y\left ( 0\right ) & =1\\ y^{\prime }\left ( 0\right ) & =2 \end{align*}

Here \(f\left ( x\right ) =\frac {1}{x}\) is not continuous at \(x=0\). Therefore theory does not apply. It turns out that no solution exists for this ode.