2.3.2 Examples
Example 1 \(\left ( x-x^{2}\right ) y^{\prime \prime }+3y^{\prime }+2y=3x^{2}\)
Example 2 \(4x^{2}y^{\prime \prime }+4xy^{\prime }+\left ( 4x^{2}-1\right ) y=0\)
Example 3 \(y^{\prime \prime }+y^{\prime }+y=\sqrt {x}\)
Example 4. \(x^{2}y^{\prime \prime }+3xy^{\prime }+4x^{4}y=0\)
Example 5. \(xy^{\prime \prime }+2y^{\prime }+xy=0,y\left ( 0\right ) =1,y^{\prime }\left ( 0\right ) =0\)