2.4.1 Examples
2.4.1.1 Example 1 \(x^{2}y^{\prime \prime }+xy^{\prime }+\left ( x^{2}-4\right ) y=0\)
2.4.1.2 Example 2 \(x^{2}y^{\prime \prime }+xy^{\prime }+\left ( x^{2}-4\right ) y=1\)
2.4.1.3 Example 3 \(x^{2}y^{\prime \prime }+xy^{\prime }+\left ( x^{2}-4\right ) y=\frac {1}{x}\)
2.4.1.4 Example 4. \(x^{2}y^{\prime \prime }-xy=0\)
2.4.1.5 Example 5. \(x^{\frac {3}{2}}y^{\prime \prime }+y=0\)
2.4.1.6 Example 6 \(xy^{\prime \prime }+y=x\)
2.4.1.7 Example 7. \(xy^{\prime \prime }-2y^{\prime }+y=\cos x\)
2.4.1.8 Example 8 \(xy^{\prime \prime }+xy^{\prime }+y=1,y\left ( 0\right ) =1\)