| # | ODE | Mathematica | Maple | Sympy |
| \[
{} \left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\]
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| \[
{} x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2} x^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\]
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| \[
{} x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0
\]
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| \[
{} x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2}
\]
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| \[
{} a \tan \left (\frac {x}{2}\right )^{2} y-\csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y+4 \coth \left (x \right ) y^{\prime }+4 x y^{\prime \prime } = 0
\]
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| \[
{} y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} x^{3} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+\left (\operatorname {b0} \,x^{4}+\operatorname {a0} \right ) y^{\prime }+x \left (a^{2}-x^{2}\right ) \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = x +6 y^{2}
\]
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| \[
{} y^{\prime \prime } = a +b x +c y^{2}
\]
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| \[
{} y^{\prime \prime } = a +x y+2 y^{3}
\]
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| \[
{} y^{\prime \prime } = f \left (x \right )+g \left (x \right ) y+2 y^{3}
\]
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| \[
{} y^{\prime \prime } = a -2 a b x y+2 y^{3} b^{2}
\]
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| \[
{} y^{\prime \prime } = \operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3}
\]
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| \[
{} a \,x^{r} y^{s}+y^{\prime \prime } = 0
\]
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| \[
{} y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+3 f \left (x \right ) y^{\prime }+y^{\prime \prime } = 2 y^{3}
\]
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| \[
{} y y^{\prime }+y^{\prime \prime } = -12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right )
\]
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| \[
{} y^{\prime \prime } = \operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = \operatorname {g3} \left (x \right )+\operatorname {g2} \left (x \right ) y+\operatorname {g1} \left (x \right ) y^{2}+\operatorname {g0} \left (x \right ) y^{3}+\left (\operatorname {f1} \left (x \right )+\operatorname {f0} \left (x \right ) y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = f^{\prime }\left (x \right ) y+\left (f \left (x \right )-2 y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = g \left (x \right )+f \left (x \right ) y^{2}+\left (f \left (x \right )-2 y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = \operatorname {f3} \left (x \right )+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = \operatorname {f4} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime }
\]
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| \[
{} 3 y y^{\prime }+y^{\prime \prime } = f \left (x \right )+g \left (x \right ) y-y^{3}
\]
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| \[
{} b y+a \left (y^{2}-1\right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} h \left (y\right )+f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = A \,x^{a} y^{b} {y^{\prime }}^{c}
\]
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| \[
{} y^{\prime \prime } = f \left (a x +b y, y^{\prime }\right )
\]
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| \[
{} y^{\prime \prime } = f \left (x , \frac {y^{\prime }}{y}\right ) y
\]
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| \[
{} y^{\prime \prime } = x^{n -2} f \left (y x^{-n}, x^{-n +1} y^{\prime }\right )
\]
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| \[
{} x y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x^{m} y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} a \,x^{m} y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (-y+a x y^{\prime }\right )^{2}+x y^{\prime \prime } = b
\]
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| \[
{} a y \left (1-y^{n}\right )+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a \,{\mathrm e}^{y-1}+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (a +1\right ) x y^{\prime }+x^{2} y^{\prime \prime } = x^{k} f \left (x^{k} y, k y+x y^{\prime }\right )
\]
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| \[
{} 2 x y+a \,x^{4} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = b
\]
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| \[
{} b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} 24+12 x y+x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right ) = 0
\]
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| \[
{} -6+x y \left (12+3 x y-2 x^{2} y^{2}\right )+x^{2} \left (9+2 x y\right ) y^{\prime }+2 x^{3} y^{\prime \prime } = 0
\]
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| \[
{} y^{b}+x^{a} y^{\prime \prime } = 0
\]
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| \[
{} 24-48 x y+\left (-12 x^{2}+1\right ) \left (y^{2}+3 y^{\prime }\right )+2 x \left (-4 x^{2}+1\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right ) = 0
\]
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| \[
{} b +a x y-\left (-12 x^{2}+k \,x^{k -1}\right ) \left (y^{2}+3 y^{\prime }\right )+2 \left (-4 x^{3}+x^{k}\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right ) = 0
\]
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| \[
{} \sqrt {x}\, y^{\prime \prime } = y^{{3}/{2}}
\]
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| \[
{} f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right )^{2} y^{\prime \prime } = g \left (y, f \left (x \right ) y^{\prime }\right )
\]
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| \[
{} f \left (x \right )^{2} y^{\prime \prime } = -24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime }
\]
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| \[
{} y y^{\prime \prime } = {\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} y-x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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| \[
{} a x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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| \[
{} y y^{\prime \prime } = y^{3}-f^{\prime }\left (x \right ) y+f \left (x \right ) y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = -f \left (x \right ) y^{3}+y^{4}-f \left (x \right ) y^{\prime }+{y^{\prime }}^{2}+y f^{\prime \prime }\left (x \right )
\]
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| \[
{} y y^{\prime \prime } = b y^{2}+y^{3}+a y y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = -y \left (f^{\prime }\left (x \right )-y^{2} g^{\prime }\left (x \right )\right )+\left (f \left (x \right )+g \left (x \right ) y^{2}\right ) y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+a {y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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| \[
{} 2 y y^{\prime \prime } = 4 y^{2} \left (2 y+x \right )+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = -1-2 x y^{2}+a y^{3}+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = y^{2} \left (a x +b y\right )+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = -a^{2}-4 \left (-x^{2}+b \right ) y^{2}+8 x y^{3}+3 y^{4}+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = 8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = -1+2 x f \left (x \right ) y^{2}-y^{4}-4 y^{2} y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = f \left (x \right ) y^{2}+3 {y^{\prime }}^{2}
\]
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| \[
{} a \left (2+a \right )^{2} y y^{\prime \prime } = -a^{2} f \left (x \right )^{2} y^{4}+a^{2} \left (2+a \right ) y^{3} f^{\prime }\left (x \right )+a \left (2+a \right )^{2} f \left (x \right ) y^{2} y^{\prime }+\left (a -1\right ) \left (2+a \right )^{2} {y^{\prime }}^{2}
\]
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| \[
{} x y y^{\prime \prime } = y \left (\operatorname {a2} +\operatorname {a3} y^{2}\right )+x \left (\operatorname {a0} +\operatorname {a1} y^{4}\right )-y y^{\prime }+x {y^{\prime }}^{2}
\]
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| \[
{} x y y^{\prime \prime } = x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2}
\]
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| \[
{} x y y^{\prime \prime } = b^{2} x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2}
\]
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| \[
{} \operatorname {f3} \left (x \right ) y^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f0} \left (x \right ) y y^{\prime \prime } = 0
\]
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| \[
{} 4 f \left (x \right ) y y^{\prime \prime } = 4 f \left (x \right )^{2} y+3 f \left (x \right ) g \left (x \right ) y^{2}-f \left (x \right ) y^{4}+2 y^{3} f^{\prime }\left (x \right )+\left (-6 f \left (x \right ) y^{2}+2 f^{\prime }\left (x \right )\right ) y^{\prime }+3 f \left (x \right ) {y^{\prime }}^{2}
\]
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| \[
{} y {y^{\prime }}^{2}+y^{2} y^{\prime \prime } = b x +a
\]
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| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime } = \left (1+y^{2}\right ) \left (x y^{\prime }-y\right )
\]
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| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime } = 2 \left (1+y^{2}\right ) \left (x y^{\prime }-y\right )
\]
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| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = 4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2}
\]
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| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = -\left (1-y\right )^{3} \left (\operatorname {F0} \left (x \right )^{2}-\operatorname {G0} \left (x \right )^{2} y^{2}\right )-4 \left (1-y\right ) y^{2} \left (f \left (x \right )^{2}-g \left (x \right )^{2}+f^{\prime }\left (x \right )+g^{\prime }\left (x \right )\right )-4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2}
\]
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| \[
{} \operatorname {a2} x \left (1-y\right ) y^{2}+\operatorname {a3} \,x^{3} y^{2} \left (1+y\right )+\left (1-y\right )^{3} \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+2 x \left (1-y\right ) y y^{\prime }-x^{2} \left (1-3 y\right ) {y^{\prime }}^{2}+2 x^{2} \left (1-y\right ) y y^{\prime \prime } = 0
\]
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| \[
{} 2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = -y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
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| \[
{} 2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = f \left (x \right ) \left (\left (1-y\right ) \left (x -y\right ) y\right )^{{3}/{2}}-y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
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| \[
{} 2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = \operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (\operatorname {a2} -1\right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
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| \[
{} y \left (1+a^{2}-2 a^{2} y^{2}\right )+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime } = 0
\]
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| \[
{} X \left (x , y\right )^{3} y^{\prime \prime } = 1
\]
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| \[
{} y^{\prime } y^{\prime \prime } = x y^{2}+x^{2} y y^{\prime }
\]
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| \[
{} y+x y^{\prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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| \[
{} y+3 x y^{\prime }+2 {y^{\prime }}^{3} y+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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|
| \[
{} h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 \left (x -y^{\prime }\right ) y^{\prime }-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2} = 2 y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2} = 4 x y \left (x y^{\prime }-y\right )^{3}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} f^{\prime }\left (x \right ) y+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -6 y+6 y^{\prime } \left (1+x \right )-3 x \left (x +2\right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|