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\[
{} \left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-a y-b = 0
\]
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\[
{} a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} 2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x y^{\prime \prime } \left (x +4 y^{\prime }\right )+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0
\]
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\[
{} 3 x^{2} {y^{\prime \prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\]
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\[
{} x^{2} \left (2-9 x \right ) {y^{\prime \prime }}^{2}-6 x \left (1-6 x \right ) y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2} = 0
\]
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\[
{} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\]
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\[
{} \left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3} = 0
\]
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\[
{} \left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3} = 0
\]
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\[
{} \sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime }-f \left (y\right ) = 0
\]
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\[
{} y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}
\]
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\[
{} y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} \left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
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\[
{} 2 y^{\prime \prime } = {\mathrm e}^{y}
\]
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\[
{} y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2} = 0
\]
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\[
{} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} x^{3} y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )-x^{2} y^{2}
\]
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\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }+y y^{\prime } = 0
\]
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\[
{} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} x \left (x +2 y\right ) y^{\prime \prime }+2 x {y^{\prime }}^{2}+4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
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\[
{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\]
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\[
{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\]
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\[
{} x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3} = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} x^{3} x^{\prime \prime }+1 = 0
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} y^{\prime \prime } = 3 \sqrt {y}
\]
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\[
{} {y^{\prime }}^{2}+y y^{\prime \prime } = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\]
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\[
{} y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\]
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\[
{} m x^{\prime \prime } = f \left (x\right )
\]
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\[
{} m x^{\prime \prime } = f \left (x^{\prime }\right )
\]
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\[
{} x y y^{\prime \prime }-x {y^{\prime }}^{2}-y y^{\prime } = 0
\]
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\[
{} x y^{\prime \prime } = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\]
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\[
{} y^{\prime \prime } = 2 y^{3}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\]
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\[
{} y^{\prime \prime }+y y^{\prime } = 1
\]
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\[
{} \sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\]
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\[
{} y y^{\prime \prime } = 1
\]
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\[
{} y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\]
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\[
{} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\]
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\[
{} \frac {x y^{\prime \prime }}{y+1}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (y+1\right )^{2}} = x \sin \left (x \right )
\]
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\[
{} \left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime } = y \sin \left (x \right )
\]
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\[
{} y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime } = \cos \left (x \right )
\]
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\[
{} \left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} \left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\]
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\[
{} y^{\prime \prime } = \frac {a}{y^{3}}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\]
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\[
{} {y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2}
\]
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\[
{} y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\]
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\[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} x^{\prime \prime }+x-x^{3} = 0
\]
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\[
{} x^{\prime \prime }+x+x^{3} = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\]
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\[
{} x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right )
\]
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\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} y^{2} y^{\prime \prime } = 8 x^{2}
\]
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\[
{} y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\]
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\[
{} y^{\prime \prime } y^{\prime } = 1
\]
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\[
{} y y^{\prime \prime } = -{y^{\prime }}^{2}
\]
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\[
{} x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime }
\]
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\[
{} x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\]
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\[
{} \left (-3+y\right ) y^{\prime \prime } = 2 {y^{\prime }}^{2}
\]
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\[
{} y y^{\prime \prime } = {y^{\prime }}^{2}
\]
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\[
{} 3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\]
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\[
{} \sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} {y^{\prime }}^{2}+y y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\]
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\[
{} y^{\prime \prime } y^{\prime } = 1
\]
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\[
{} x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime }
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\]
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\[
{} y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\]
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\[
{} \left (-3+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right )
\]
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\[
{} 2 x y^{\prime } y^{\prime \prime } = {y^{\prime }}^{2}-1
\]
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\[
{} 3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\]
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\[
{} y y^{\prime \prime }+2 {y^{\prime }}^{2} = 3 y y^{\prime }
\]
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\[
{} y^{\prime \prime } = -y^{\prime } {\mathrm e}^{-y}
\]
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\[
{} y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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