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\[
{} 4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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\[
{} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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\[
{} x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} = a
\]
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\[
{} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\]
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\[
{} y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\]
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\[
{} y = \frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}}
\]
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\[
{} \left (x y^{\prime }-y\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\]
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\[
{} 4 x {y^{\prime }}^{2}+4 y y^{\prime } = y^{4}
\]
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\[
{} 2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x = 0
\]
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\[
{} \left (x y^{\prime }-y\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\]
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\[
{} a^{2} y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\]
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\[
{} x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\]
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\[
{} \left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\]
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\[
{} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+a^{4} = 0
\]
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\[
{} x +y y^{\prime } = a {y^{\prime }}^{2}
\]
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\[
{} x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\]
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\[
{} 2 y = x y^{\prime }+\frac {a}{y^{\prime }}
\]
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\[
{} y = a y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} \left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-y^{2} a +c \right ) y^{\prime } = 0
\]
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\[
{} y = a y^{\prime }+b {y^{\prime }}^{2}
\]
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\[
{} {y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 x y-2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y} = 0
\]
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\[
{} \left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = 1
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\]
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\[
{} x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\]
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\[
{} y^{2}-2 x y y^{\prime }+\left (x^{2}-1\right ) {y^{\prime }}^{2} = m
\]
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\[
{} y = x y^{\prime }-{y^{\prime }}^{2}
\]
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\[
{} 4 {y^{\prime }}^{2} = 9 x
\]
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\[
{} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0
\]
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\[
{} \left (8 {y^{\prime }}^{3}-27\right ) x = \frac {12 {y^{\prime }}^{2}}{x}
\]
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\[
{} 3 y = 2 x y^{\prime }-\frac {2 {y^{\prime }}^{2}}{x}
\]
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\[
{} {y^{\prime }}^{2}+y^{2} = 1
\]
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\[
{} {y^{\prime }}^{2} \left (2-3 y\right )^{2} = 4-4 y
\]
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\[
{} 4 x {y^{\prime }}^{2} = \left (3 x -1\right )^{2}
\]
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\[
{} x {y^{\prime }}^{2}-\left (-a +x \right )^{2} = 0
\]
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\[
{} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
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\[
{} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\]
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\[
{} {y^{\prime }}^{2}+2 y^{\prime } x^{3}-4 x^{2} y = 0
\]
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\[
{} y^{2} \left (y-x y^{\prime }\right ) = x^{4} {y^{\prime }}^{2}
\]
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\[
{} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2} = 0
\]
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\[
{} {y^{\prime }}^{4} = 4 y \left (x y^{\prime }-2 y\right )^{2}
\]
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\[
{} \left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\]
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\[
{} y+x^{2} = {y^{\prime }}^{2}
\]
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\[
{} {y^{\prime }}^{3} = y^{4} \left (x y^{\prime }+y\right )
\]
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\[
{} \left (1-y^{\prime }\right )^{2}-{\mathrm e}^{-2 y} = {\mathrm e}^{-2 x} {y^{\prime }}^{2}
\]
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\[
{} a x y {y^{\prime }}^{2}+\left (x^{2}-y^{2} a -b \right ) y^{\prime }-x y = 0
\]
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\[
{} {y^{\prime }}^{2} = \left (1+4 y\right ) \left (y^{\prime }-y\right )
\]
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\[
{} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+b^{2}-y^{2} = 0
\]
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\[
{} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+x y = 0
\]
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\[
{} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-x y = 0
\]
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\[
{} 8 x {y^{\prime }}^{3} = y \left (12 {y^{\prime }}^{2}-9\right )
\]
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\[
{} 4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2} = 0
\]
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\[
{} \left (x^{2} y^{\prime }+y^{2}\right ) \left (x y^{\prime }+y\right ) = \left (1+y^{\prime }\right )^{2}
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\]
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\[
{} {y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0
\]
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\[
{} x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2} = x^{4}+2 x y y^{\prime }
\]
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\[
{} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x = 0
\]
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\[
{} {y^{\prime }}^{3} \left (x +2 y\right )+3 {y^{\prime }}^{2} \left (x +y\right )+\left (y+2 x \right ) y^{\prime } = 0
\]
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\[
{} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b
\]
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\[
{} y = \frac {x}{y^{\prime }}-a y^{\prime }
\]
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\[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
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\[
{} x {y^{\prime }}^{3} = a +b y^{\prime }
\]
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\[
{} y^{\prime } = \tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right )
\]
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\[
{} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\]
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\[
{} y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\]
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\[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
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\[
{} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\]
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\[
{} y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\]
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\[
{} y-2 x y^{\prime }+a y {y^{\prime }}^{2} = 0
\]
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\[
{} x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\]
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\[
{} x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3}
\]
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\[
{} 3 y {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\]
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\[
{} \left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\]
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\[
{} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{2} \left (-x^{2}+1\right ) = 1-y^{2}
\]
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\[
{} y^{2} \left (1+{y^{\prime }}^{2}\right ) = r^{2}
\]
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\[
{} \sin \left (x y^{\prime }\right ) \cos \left (y\right ) = \cos \left (x y^{\prime }\right ) \sin \left (y\right )+y^{\prime }
\]
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\[
{} 4 x {y^{\prime }}^{2} = \left (3 x -a \right )^{2}
\]
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\[
{} 4 {y^{\prime }}^{2} x \left (-a +x \right ) \left (x -b \right ) = \left (3 x^{2}-2 x \left (a +b \right )+a b \right )^{2}
\]
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\[
{} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\]
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\[
{} {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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\[
{} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\]
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\[
{} x^{2} {y^{\prime }}^{3}+y y^{\prime } \left (y+2 x \right )+y^{2} = 0
\]
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\[
{} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0
\]
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\[
{} {y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2} = 0
\]
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\[
{} \left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (x^{2}+2 x y+y^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\]
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