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\[
{} x^{2} y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} y^{\prime \prime }-y^{2} = 0
\]
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\[
{} y^{\prime \prime }-6 y^{2} = 0
\]
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\[
{} y^{\prime \prime }-6 y^{2}-x = 0
\]
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\[
{} y^{\prime \prime }-6 y^{2}+4 y = 0
\]
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\[
{} y^{\prime \prime }+y^{2} a +b x +c = 0
\]
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\[
{} y^{\prime \prime }-2 y^{3}-x y+a = 0
\]
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\[
{} y^{\prime \prime }-a y^{3} = 0
\]
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\[
{} y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b = 0
\]
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\[
{} y^{\prime \prime }+d +b x y+c y+a y^{3} = 0
\]
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\[
{} y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{r} y^{2} = 0
\]
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\[
{} y^{\prime \prime }+6 a^{10} y^{11}-y = 0
\]
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\[
{} y^{\prime \prime }-\frac {1}{\left (y^{2} a +b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0
\]
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\[
{} y^{\prime \prime }-{\mathrm e}^{y} = 0
\]
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\[
{} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0
\]
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\[
{} y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0
\]
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\[
{} y^{\prime \prime }+a \sin \left (y\right ) = 0
\]
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\[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0
\]
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\[
{} y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0
\]
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\[
{} y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y = 0
\]
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\[
{} y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0
\]
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\[
{} y^{\prime \prime }+y y^{\prime }-y^{3} = 0
\]
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\[
{} y^{\prime \prime }+y y^{\prime }-y^{3}+a y = 0
\]
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\[
{} y^{\prime \prime }+\left (y+3 a \right ) y^{\prime }-y^{3}+y^{2} a +2 a^{2} y = 0
\]
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\[
{} y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+y^{2} f \left (x \right )+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right ) = 0
\]
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\[
{} y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime }-3 y y^{\prime }-3 y^{2} a -4 a^{2} y-b = 0
\]
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\[
{} y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime }-2 a y y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+a y y^{\prime }+b y^{3} = 0
\]
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\[
{} y^{\prime \prime }+a {y^{\prime }}^{2}+b y = 0
\]
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\[
{} y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{\prime }+c y = 0
\]
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\[
{} y^{\prime \prime }+a {y^{\prime }}^{2}+b \sin \left (y\right ) = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0
\]
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\[
{} y^{\prime \prime }+a y {y^{\prime }}^{2}+b y = 0
\]
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\[
{} y^{\prime \prime }+a y \left (1+{y^{\prime }}^{2}\right )^{2} = 0
\]
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\[
{} y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{v} = 0
\]
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\[
{} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0
\]
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\[
{} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b
\]
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\[
{} y^{\prime \prime } = a \sqrt {{y^{\prime }}^{2}+b y^{2}}
\]
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\[
{} y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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\[
{} y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
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\[
{} y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
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\[
{} y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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\[
{} y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0
\]
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\[
{} 8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\]
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\[
{} x y^{\prime \prime }+\left (-1+y\right ) y^{\prime } = 0
\]
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\[
{} x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0
\]
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\[
{} x y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b = 0
\]
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\[
{} 2 x y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\]
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\[
{} x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b \,x^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0
\]
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\[
{} x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0
\]
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\[
{} 9 x^{2} y^{\prime \prime }+a y^{3}+2 y = 0
\]
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\[
{} x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0
\]
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\[
{} x^{3} y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} 2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0
\]
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\[
{} 2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0
\]
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\[
{} x^{4} y^{\prime \prime }+a^{2} y^{n} = 0
\]
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\[
{} x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2} = 0
\]
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\[
{} x^{4} y^{\prime \prime }-x^{2} \left (x +y^{\prime }\right ) y^{\prime }+4 y^{2} = 0
\]
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\[
{} x^{4} y^{\prime \prime }+\left (x y^{\prime }-y\right )^{3} = 0
\]
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\[
{} \sqrt {x}\, y^{\prime \prime }-y^{{3}/{2}} = 0
\]
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\[
{} \left (a \,x^{2}+b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {a \,x^{2}+b x +c}}\right ) = 0
\]
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\[
{} y y^{\prime \prime }-a = 0
\]
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\[
{} y y^{\prime \prime }-a x = 0
\]
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\[
{} y y^{\prime \prime }-a \,x^{2} = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-a = 0
\]
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\[
{} y y^{\prime \prime }+y^{2}-a x -b = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} \ln \left (y\right ) = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3} = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-f^{\prime \prime }\left (x \right ) y+f \left (x \right ) y^{3}-y^{4} = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2} = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 y^{2} a +b y^{3} = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 a^{2} y^{2}-2 b^{2} y^{3}+a y = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (y+1\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0
\]
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