2.12.1 Examples

2.12.1.1 Example 1 \(y^{\prime }=\frac {-y\left ( 2x^{2}y^{3}+3\right ) }{x\left ( x^{2}y^{3}+1\right ) }\)
2.12.1.2 Example 2 \(y^{\prime }=\frac {2x\left ( -x^{4}-2x^{2}y+y^{2}\right ) }{y^{2}+2x^{2}y-x^{4}}\)
2.12.1.3 Example 3 \(y^{\prime }=-\frac {1}{2}\frac {3y^{2}-x}{y\left ( y^{2}-3x\right ) }\)
2.12.1.4 Example 4 \(y^{\prime }=-\frac {1}{2}\frac {y\left ( 1+\sqrt {x^{2}y^{4}+1}\right ) }{x}\)
2.12.1.5 Example 5 \(y^{\prime }=x\left ( 1+\frac {2y}{x}+\frac {y^{2}}{x^{4}}\right ) \)
2.12.1.6 Example 6 \(\left ( y^{\prime }\right ) ^{2}=4y-x^{2}\)
2.12.1.7 Example 7 \(y^{\prime }=\frac {ay^{n}+bx^{n\left ( m+1\right ) }}{x^{nm-m+n}}\)