| # | ODE | Mathematica | Maple | Sympy |
| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} y b^{2}+x \left (a^{2}+2 x^{2}\right ) y^{\prime }+x^{2} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0
\]
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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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| \[
{} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime } = 0
\]
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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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| \[
{} -2 \left (1-x \right ) y+2 \left (3-x \right ) x \left (1+x \right ) y^{\prime }+\left (1-x \right ) x \left (1+x \right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -y+\left (1-2 x \right ) \left (1-x \right ) x y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (1-x \right ) x \left (\operatorname {b2} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
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| \[
{} b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = k^{2} y
\]
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| \[
{} B y+\left (a -x \right ) \left (-x +b \right ) \left (A +2 x \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} -y-2 \left (a -x \right )^{3} y^{\prime }+\left (a -x \right )^{4} y^{\prime \prime } = 0
\]
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| \[
{} 2 \left (3 x +1\right ) y+2 \left (2-3 x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
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| \[
{} 2 \left (1-x \right ) y+2 \left (1-2 x \right ) \left (2-x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (4 k^{2}+\left (4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (4 k^{2}+\left (-4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (a \left (a +1\right ) \left (1-x \right )+b^{2} x \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) x y^{\prime }+4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} y+\left (b x +a \right )^{4} y^{\prime \prime } = 0
\]
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| \[
{} A y+\left (c \,x^{2}+b x +a \right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} -y+x y^{\prime }+x^{5} y^{\prime \prime } = 0
\]
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| \[
{} \left (-2 x^{3}+1\right ) y-x \left (-2 x^{3}+1\right ) y^{\prime }+x^{5} y^{\prime \prime } = 0
\]
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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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| \[
{} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
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| \[
{} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
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| \[
{} y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (-x +b \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} \left (c -x \right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (-2 x^{2}+1\right ) y+4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
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| \[
{} \left (8 x^{4}+10 x^{2}+1\right ) y-4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
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| \[
{} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
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| \[
{} \left (1-a \right )^{2} y+a \,x^{2 a -1} y^{\prime }+x^{2 a} y^{\prime \prime } = 0
\]
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| \[
{} a^{2} x^{a -1} y+\left (-2 a +1\right ) x^{a} y^{\prime }+x^{a +1} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a2} +\operatorname {b2} \,x^{k}\right ) y+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) y^{\prime }+x^{2} \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}\right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} -\left (4 k^{2}-\left (-p^{2}+1\right ) \sinh \left (x \right )^{2}\right ) y+4 \cosh \left (x \right ) \sinh \left (x \right ) y^{\prime }+4 \sinh \left (x \right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2} a +2\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (1+y^{\prime }\right ) x = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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| \[
{} u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}} = 0
\]
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| \[
{} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0
\]
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| \[
{} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0
\]
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| \[
{} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0
\]
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| \[
{} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0
\]
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| \[
{} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0
\]
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| \[
{} -a^{2} y+y^{\prime \prime } = \frac {6 y}{x^{2}}
\]
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| \[
{} y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}
\]
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| \[
{} y^{\prime \prime }+y \,{\mathrm e}^{2 x} = n^{2} y
\]
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| \[
{} y^{\prime \prime }+\frac {y}{4 x} = 0
\]
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| \[
{} x y^{\prime \prime }+y^{\prime }+y = 0
\]
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| \[
{} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\]
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| \[
{} y^{\prime \prime }+2 x y^{\prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+6 y = 0
\]
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| \[
{} \left (2-x \right ) x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
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| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+\left (x +2\right ) y = 0
\]
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| \[
{} 3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )-y = 0
\]
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| \[
{} x \left (1+x \right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\]
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| \[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+2 y = 0
\]
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| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\]
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| \[
{} x \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (-x^{2}+1\right )+\left (x -1\right ) y = 0
\]
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| \[
{} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\]
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| \[
{} x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
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| \[
{} 2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\]
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| \[
{} x y^{\prime \prime }+x y^{\prime }-2 y = 0
\]
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| \[
{} x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y = 0
\]
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| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\]
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| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0
\]
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| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0
\]
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| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0
\]
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| \[
{} x y^{\prime \prime }-y^{\prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y = 0
\]
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| \[
{} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0
\]
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| \[
{} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\]
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