| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x y^{\prime } = a y^{3}+3 a b \,x^{n} y^{2}-b n \,x^{n}-2 a \,b^{3} x^{3 n}
\]
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| \[
{} x y^{\prime } = 3 x^{2 n +1} y^{3}+\left (b x -n \right ) y+c \,x^{-n +1}
\]
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| \[
{} x y^{\prime } = a \,x^{n +2} y^{3}+\left (b \,x^{n}-1\right ) y+c \,x^{n -1}
\]
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| \[
{} x^{2} y^{\prime } = y^{3}-3 y a^{2} x^{4}+2 a^{3} x^{6}+2 a \,x^{3}
\]
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| \[
{} y^{\prime } = -\left (a x +b \,x^{m}\right ) y^{3}+y^{2}
\]
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| \[
{} y^{\prime } = \frac {y^{3}}{\sqrt {x^{2} a +b x +c}}+y^{2}
\]
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| \[
{} y^{\prime } = -\frac {\left (a x -\frac {6}{25}\right )^{{34}/{9}} y^{3}}{x^{{16}/{9}}}+\frac {\frac {2 a x}{3}-\frac {4}{675}}{x^{{11}/{18}} \left (a x -\frac {6}{25}\right )^{{61}/{18}}}
\]
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| \[
{} y^{\prime } = -y^{3}+a \,{\mathrm e}^{\lambda x} y^{2}
\]
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| \[
{} y^{\prime } = -y^{3}+3 a^{2} {\mathrm e}^{2 \lambda x} y-2 a^{3} {\mathrm e}^{3 \lambda x}+a \lambda \,{\mathrm e}^{\lambda x}
\]
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| \[
{} y^{\prime } = a \,{\mathrm e}^{2 \lambda x} y^{3}+b \,{\mathrm e}^{\lambda x} y^{2}+c y+d \,{\mathrm e}^{-\lambda x}
\]
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| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\lambda x} y^{2}+c y-2 a \,b^{3} {\mathrm e}^{\lambda x}+b c
\]
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| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y^{2}-2 a \,b^{3} {\mathrm e}^{\left (\lambda +3 \mu \right ) x}-b \mu \,{\mathrm e}^{x \mu }
\]
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| \[
{} y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\]
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| \[
{} y^{\prime \prime }-\left (x^{2} a +b \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0
\]
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| \[
{} y^{\prime \prime }-\left (x^{2} a +b c x \right ) y = 0
\]
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| \[
{} y^{\prime \prime }-a \,x^{n} y = 0
\]
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| \[
{} y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y = 0
\]
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| \[
{} 2 n y-2 x y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} b y+a x y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }+a x y^{\prime }+b x y = 0
\]
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| \[
{} y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+2 a x y^{\prime }+\left (x^{4} b +a^{2} x^{2}+c x +a \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (x^{2} a +b \right ) y^{\prime }+c \left (x^{2} a +b -c \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (x^{2} a +2 b \right ) y^{\prime }+\left (a b \,x^{2}-a x +b^{2}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+x^{2} a +b +2 x \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a b \,x^{2}+b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+x \left (a b \,x^{2}+b c +2 a \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (a \,x^{3} b +a c \,x^{2}+b \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a \,x^{3} b -x^{2} a +b^{2}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 x^{2} a +b \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{3} b +b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y = 0
\]
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| \[
{} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{m +n}+b \,x^{2 m}+m \,x^{m -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+a n \,x^{n -1}+c \,x^{m -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+x^{n} \left (x^{2} a +\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (1+m \right ) x^{m -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{m +n}+b \left (1+m \right ) x^{m -1}-a \,x^{n -1}\right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{m +n}+b c \,x^{m}+a n \,x^{n -1}\right ) y = 0
\]
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| \[
{} b y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} b x y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+n y^{\prime }+b \,x^{-2 n +1} y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{-1+2 n} y = 0
\]
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| \[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{n} y = 0
\]
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| \[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+a x y^{\prime }+a y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (-x +b \right ) y^{\prime }-a y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y = 0
\]
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| \[
{} \left (a b x +a n +b m \right ) y+\left (m +n +x \left (a +b \right )\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\]
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✓ |
✓ |
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| \[
{} x y^{\prime \prime }-\left (a x +1\right ) y^{\prime }-b \,x^{2} \left (b x +a \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right ) = 0
\]
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✓ |
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| \[
{} x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (a b \,x^{2}+b -5\right ) y^{\prime }+2 a^{2} \left (b -2\right ) x^{3} y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }-\left (a c \,x^{2}+\left (b c +c^{2}+a \right ) x +b +2 c \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x^{2} a +b x +2\right ) y^{\prime }+b y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (2 a x +b \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x^{2} a +b x +2\right ) y^{\prime }+\left (c \,x^{2}+d x +b \right ) y = 0
\]
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✓ |
✓ |
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| \[
{} x y^{\prime \prime }+\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y = 0
\]
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✓ |
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| \[
{} x y^{\prime \prime }+\left (x^{2} a +b \right ) x y^{\prime }+\left (3 x^{2} a +b \right ) y = 0
\]
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✓ |
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| \[
{} x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+2\right ) y^{\prime }+b x y = 0
\]
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✓ |
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| \[
{} x y^{\prime \prime }+\left (a \,x^{3} b +b \,x^{2}+a x -1\right ) y^{\prime }+a^{2} b \,x^{3} y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (x^{2} a +b x +c \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y = 0
\]
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✓ |
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| \[
{} x y^{\prime \prime }+\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{-1+2 n} y = 0
\]
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