3.4.10.1 Example 1 on how to find Lie group \(\left ( x,y\right ) \) given Lie infinitesimal xi and eta
3.4.10.2 Example how to find Lie group \(\left ( x,y\right ) \) given canonical coordinates \(R,S\)
3.4.10.3 Example \(y^{\prime }=\frac {y}{x}+x\)
3.4.10.4 Example \(y^{\prime }=xy^{2}-\frac {2y}{x}-\frac {1}{x^{3}}\)
3.4.10.5 Example \(y^{\prime }=\frac {y+1}{x}+\frac {y^{2}}{x^{3}}\)
3.4.10.6 Example \(y^{\prime }=\frac {y-4xy^{2}-16x^{3}}{y^{3}+4x^{2}y+x}\)
3.4.10.7 Example \(y^{\prime }=\frac {-y^{2}}{e^{x}-y}\)
3.4.10.8 Example \(y^{\prime }=\frac {x\sqrt {1+y}+\sqrt {1+y}+1+y}{1+x}\)
3.4.10.9 Example \(y^{\prime }=\frac {-y}{2x-ye^{y}}\)
3.4.10.10 Example \(y^{\prime }=\frac {-1-2yx}{x^{2}+2y}\)
3.4.10.11 Example \(y^{\prime }=3\sqrt {yx}\)
3.4.10.12 Example \(y^{\prime }=4\left ( yx\right ) ^{\frac {1}{3}}\)
3.4.10.13 Example \(y^{\prime }=2y+3e^{2x}\)
3.4.10.14 Example \(y^{\prime }=\frac {1}{3}\frac {2y+y^{3}-x^{2}}{x}\)
3.4.10.15 Example \(y^{\prime }=3-2\frac {y}{x}\)
3.4.10.16 Example \(y^{\prime }=\frac {-3+\frac {y}{x}}{-1-\frac {y}{x}}\)
3.4.10.17 Example \(y^{\prime }=\frac {1+3\left ( \frac {y}{x}\right ) ^{2}}{2\frac {y}{x}}\)
3.4.10.18 Example \(y^{\prime }=\frac {y}{x}+\frac {1}{x}F\left ( \frac {y}{x}\right ) \)
3.4.10.19 Example \(y^{\prime }=\frac {y}{x}+\frac {1}{x}e^{-\frac {y}{x}}\)
3.4.10.20 Example \(y^{\prime }=\frac {1-y^{2}+x^{2}}{1+y^{2}-x^{2}}\)
3.4.10.21 Example \(y^{\prime }=-\frac {1}{4}xe^{-2y}+\frac {1}{4}\sqrt {\left ( e^{-2y}\right ) ^{2}x^{2}+4e^{-2y}}\)
3.4.10.22 Example \(y^{\prime }=\frac {y-xf\left ( x^{2}+ay^{2}\right ) }{x+ayf\left ( x^{2}+ay^{2}\right ) }\)