| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2-x
\]
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| \[
{} \left (a^{2} x^{2}+2\right ) y-2 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (n \left (n +1\right )-a^{2} x^{2}\right ) y+2 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (b \,x^{2}+a \right ) y+2 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a y-2 \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = a -x +x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 5 x
\]
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| \[
{} -5 y-3 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -5 y-3 x y^{\prime }+x^{2} y^{\prime \prime } = x^{2} \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
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| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (1+x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{2} \left (x^{2}-1\right )
\]
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| \[
{} \left (-x^{2}+2\right ) y+4 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{2}+6\right ) y+4 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} 13 y+5 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} 16 y-7 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} \,x^{2}+\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (c \,x^{3}+b \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{2} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (b +c \,x^{2 k}\right ) y+a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} c y+\left (b x +a \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = {\mathrm e}^{x} x^{2+a}
\]
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| \[
{} \left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (b x +a \right ) y+2 a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -2 x^{2} y-x^{2} y^{\prime }+x^{2} y^{\prime \prime } = 1+x +2 x^{2} \ln \left (x \right )
\]
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| \[
{} \left (b \,x^{2}+a \right ) y+x^{2} y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -y-y^{\prime } \left (-x^{2}+1\right )+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (1-x \right ) y+x \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
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| \[
{} -\left (2+3 x \right ) y+\left (2-x \right ) x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} 2 \left (1+x \right ) y-2 x \left (1+x \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -2 y+a \,x^{2} y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (3 a x +5\right ) y-x \left (a x +5\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (-x^{2}+2\right ) y+x^{3} y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (x^{2}+1\right ) y+x \left (-x^{2}+1\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (4 x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+\operatorname {c1} \,x^{2 k}\right ) y+x \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a y+2 x^{2} \cot \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (a -x \cot \left (x \right )\right ) y+x \left (1+2 x \cot \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a y-2 x^{2} \tan \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (a +x \tan \left (x \right )\right ) y+x \left (1-2 x \tan \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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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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| \[
{} -2 y+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} a -x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = x
\]
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| \[
{} y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
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| \[
{} 3 y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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| \[
{} n^{2} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} a^{2} y+x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} a^{2} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (b \,x^{2}+a \right ) y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} a -2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -2 y+2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (-x^{2}+1\right )^{2}
\]
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| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = \frac {2 \left (-n -1\right ) x \operatorname {LegendreP}\left (n , x\right )+2 \left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )}{x^{2}-1}
\]
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| \[
{} -p \left (p +1\right ) y+2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} p \left (p +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} n \left (n +2\right ) y-3 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -a y-3 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} 2 y+4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = -2 x +2 \cos \left (x \right )
\]
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| \[
{} 6 y-4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -\left (x^{2}+1\right ) y-4 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -4 y-6 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} n \left (1+a +b +n \right ) y+\left (-a +b -\left (2+a +b \right ) x \right ) y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} p \left (2 k +p \right ) y-\left (1+2 k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} p \left (1+2 k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -\left (k -p \right ) \left (1+k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (1-a \right ) a y-2 a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -\left (2-a \right ) y+a x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} b y+a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y+a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} c y+\left (b x +a \right ) y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} \left (c^{2} x^{2}+b^{2}\right ) y-x y^{\prime }+\left (a^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} -12 y-8 x y^{\prime }+\left (a^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} y+2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
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| \[
{} 2 y-2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} 6 y+2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} 6 y-2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
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