2.5.2 Examples
2.5.2.1 Example 1 \(2x^{2}y^{\prime \prime }+3xy^{\prime }-xy=x^{2}+2x\)
2.5.2.2 Example 2 \(2xy^{\prime \prime }+\left ( x+1\right ) y^{\prime }+3y=5\)
2.5.2.3 Example 3 \(2xy^{\prime \prime }+\left ( x+1\right ) y^{\prime }+3y=x\)
2.5.2.4 Example 4 \(x^{2}y^{\prime \prime }+\left ( x+1\right ) y^{\prime }+y=5\)
2.5.2.5 Example 5 \(2x^{2}y^{\prime \prime }-xy^{\prime }+\left ( 1-x^{2}\right ) y=x^{2}\)
2.5.2.6 Example 6 \(2xy^{\prime \prime }+y^{\prime }+y=0\)
2.5.2.7 Example 7 \(4xy^{\prime \prime }+3y^{\prime }+3y=\sqrt {x}\)
2.5.2.8 Example 8. \(2x^{2}y^{\prime \prime }\left ( x\right ) -xy^{\prime }\left ( x\right ) +\left ( 1-x^{2}\right ) y\left ( x\right ) =0\)
2.5.2.9 Example 9. \(2x^{2}y^{\prime \prime }\left ( x\right ) -xy^{\prime }\left ( x\right ) +\left ( 1-x^{2}\right ) y\left ( x\right ) =1+x\)