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\[
{} y^{\prime \prime } = -\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}}
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime }-\left (a^{2} \cos \left (x \right )^{2}+b \cos \left (x \right )+\frac {b^{2}}{\left (2 a -3\right )^{2}}+3 a +2\right ) y = 0
\]
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\[
{} y^{\prime \prime } = -\frac {\left (-\left (a^{2} b^{2}-\left (a +1\right )^{2}\right ) \sin \left (x \right )^{2}-a \left (a +1\right ) b \sin \left (2 x \right )-a \left (a -1\right )\right ) y}{\sin \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (a \cos \left (x \right )^{2}+b \sin \left (x \right )^{2}+c \right ) y}{\sin \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}+\frac {y}{\sin \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = \frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}-2 y
\]
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\[
{} y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )}
\]
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\[
{} y^{\prime \prime } = -\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = \frac {\left (3 \sin \left (x \right )^{2}+1\right ) y^{\prime }}{\cos \left (x \right ) \sin \left (x \right )}+\frac {\sin \left (x \right )^{2} y}{\cos \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )}
\]
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\[
{} y^{\prime \prime } = -\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (2 f \left (x \right ) {g^{\prime }\left (x \right )}^{2} g \left (x \right )-\left (g \left (x \right )^{2}-1\right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )\right ) y^{\prime }}{f \left (x \right ) g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}-\frac {\left (\left (g \left (x \right )^{2}-1\right ) \left (f^{\prime }\left (x \right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )-f \left (x \right ) f^{\prime \prime }\left (x \right ) g^{\prime }\left (x \right )\right )-\left (2 f^{\prime }\left (x \right ) g \left (x \right )+v \left (v +1\right ) f \left (x \right ) g^{\prime }\left (x \right )\right ) f \left (x \right ) {g^{\prime }\left (x \right )}^{2}\right ) y}{f \left (x \right )^{2} g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (x -1\right ) y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}}
\]
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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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\[
{} x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0
\]
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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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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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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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