2.2.2 Examples
Example 1. \(x^{2}y^{\prime \prime }\left ( x\right ) +xy^{\prime }\left ( x\right ) +x^{2}y\left ( x\right ) =0\)
Example 2. \(x^{2}y^{\prime \prime }+xy^{\prime }+x^{2}y=\sin \left ( x\right ) \)
Example 3. \(\left ( e^{x}-1\right ) y^{\prime \prime }+e^{x}y^{\prime }+y=0\)
Example 4 \(x^{2}y^{\prime \prime }+xy^{\prime }+xy=0\)
Example 5 \(x^{2}y^{\prime \prime }+xy^{\prime }+xy=1\)
Example 6 \(x^{2}y^{\prime \prime }+xy^{\prime }+xy=\frac {1}{x}\)
Example 7 \(x^{2}y^{\prime \prime }+xy^{\prime }+xy=x\)
Example 8 \(xy^{\prime \prime }+y^{\prime }-xy=0\)
Example 9 \(\sin \left ( x\right ) y^{\prime \prime }+y^{\prime }+y=0\)