6.4 Example 4. \(xy^{\prime }+y=k\)

\begin{equation} xy^{\prime }+y=k \tag {1}\end{equation}

This is similar to above example. Carrying out same steps shows that \(c_{0}=k\) and all other \(c_{n}=0\). Hence \(y_{p}=k\). The solution is

\begin{align*} y & =y_{h}+y_{p}\\ & =\frac {a_{0}}{x}+k \end{align*}