4.9.1.1 Examples
4.9.1.1.1 Example 1 \(yy^{\prime \prime }-\left ( y^{\prime }\right ) ^{2}=1\)
4.9.1.1.2 Example 2 \(y^{\prime \prime }+ay\left ( y^{\prime }\right ) +by^{3}=0\)
4.9.1.1.3 Example 3 \(2yy^{\prime \prime }-y^{3}-2\left ( y^{\prime }\right ) ^{2}=0,y\left ( 0\right ) =-1,y^{\prime }\left ( 0\right ) =0\)
4.9.1.1.4 Example 4 \(2y^{\prime \prime }-e^{y}=0,y\left ( 0\right ) =0,y^{\prime }\left ( 0\right ) =1\)
4.9.1.1.5 Example 5 \(2y^{\prime \prime }-e^{y}=0,y\left ( 0\right ) =0,y^{\prime }\left ( 0\right ) =1\)
4.9.1.1.6 Example 6 \(2y^{\prime \prime }-\sin \left ( 2y\right ) =0,y\left ( 0\right ) =-\frac {\pi }{2},y^{\prime }\left ( 0\right ) =1\)
4.9.1.1.7 Example 7 \(yy^{\prime \prime }-\left ( y^{\prime }\right ) ^{2}+\left ( y^{\prime }\right ) ^{3}=0,y\left ( 0\right ) =-1,y^{\prime }\left ( 0\right ) =0\)
4.9.1.1.8 Example 8 \(\left ( 1+\left ( y^{\prime }\right ) ^{2}\right ) ^{2}=y^{2}y^{\prime \prime },y\left ( 0\right ) =3,y^{\prime }\left ( 0\right ) =\sqrt {2}\)
4.9.1.1.9 Example 9 \(y\left ( y^{\prime \prime }\right ) ^{3}+y^{3}y^{\prime }=0\)
4.9.1.1.10 Example 10 \(yy^{\prime \prime }=2\left ( y^{\prime }\right ) ^{2}+y^{2}\)
4.9.1.1.11 Example 11 \(y^{\prime \prime }+\left ( y^{\prime }\right ) ^{2}+y^{\prime }=0,y^{\prime }\left ( 1\right ) =3\)
4.9.1.1.12 Example 12 \(y^{\prime \prime }=\left ( y^{\prime }\right ) ^{3}-\left ( y^{\prime }\right ) ^{2},y\left ( 0\right ) =3,y^{\prime }\left ( 0\right ) =1\)
4.9.1.1.13 Example 13 \(y^{\prime \prime }=-e^{-2y}=0,y\left ( 3\right ) =0,y^{\prime }\left ( 3\right ) =1\)
4.9.1.1.14 Example 14 \(y^{\prime \prime }=-e^{-2y}=0,y\left ( 3\right ) =0,y^{\prime }\left ( 3\right ) =-1\)