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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }-l y = 0
\]
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\[
{} x \left (x +2\right ) y^{\prime \prime }+2 \left (n +1+\left (n +1-2 l \right ) x -l \,x^{2}\right ) y^{\prime }+\left (2 l \left (p -n -1\right ) x +2 p l +m \right ) y = 0
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (x^{2}+x -1\right ) y^{\prime }-\left (x +2\right ) y = 0
\]
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\[
{} \left (x^{2}+3 x +4\right ) y^{\prime \prime }+\left (x^{2}+x +1\right ) y^{\prime }-\left (2 x +3\right ) y = 0
\]
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\[
{} \left (x -1\right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y = 0
\]
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\[
{} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y = 0
\]
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\[
{} 2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y = 0
\]
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\[
{} 2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y = 0
\]
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\[
{} 2 x \left (x -1\right ) y^{\prime \prime }+\left (\left (2 v +5\right ) x -2 v -3\right ) y^{\prime }+\left (v +1\right ) y = 0
\]
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\[
{} \left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+\left (4 a^{2} x^{2}+1\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-v^{2}+x \right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2 \left (1-m +2 l \right ) x -m^{2}+1\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (a \,x^{2}+1\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+f \left (x \right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (4 x^{2}+12 x +3\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y = 0
\]
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\[
{} x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (a -1\right ) y = 0
\]
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\[
{} 9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y = 0
\]
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\[
{} 16 x^{2} y^{\prime \prime }+\left (3+4 x \right ) y = 0
\]
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\[
{} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }-\left (5+4 x \right ) y = 0
\]
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\[
{} \left (27 x^{2}+4\right ) y^{\prime \prime }+27 x y^{\prime }-3 y = 0
\]
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\[
{} 48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y = 0
\]
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\[
{} 50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y = 0
\]
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\[
{} 144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y = 0
\]
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\[
{} 144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y = 0
\]
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\[
{} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+\left (c \,x^{2}+d x +f \right ) y = 0
\]
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\[
{} \operatorname {a2} \,x^{2} y^{\prime \prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x \right ) y^{\prime }+\left (\operatorname {a0} \,x^{2}+\operatorname {b0} x +\operatorname {c0} \right ) y = 0
\]
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\[
{} \left (a \,x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+b y = 0
\]
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\[
{} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime } = 0
\]
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\[
{} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y = 0
\]
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\[
{} \left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y = 0
\]
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\[
{} \operatorname {A2} \left (a x +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (a x +b \right ) y^{\prime }+\operatorname {A0} \left (a x +b \right ) y = 0
\]
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\[
{} \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +f \right ) y^{\prime }+g y = 0
\]
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\[
{} x^{3} y^{\prime \prime }+x y^{\prime }-\left (2 x +3\right ) y = 0
\]
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\[
{} x^{3} y^{\prime \prime }+2 x y^{\prime }-y = 0
\]
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\[
{} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+\left (a \,x^{2}+b x +a \right ) y = 0
\]
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\[
{} x^{3} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-2 y = 0
\]
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\[
{} x^{3} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+x y = 0
\]
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\[
{} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 x^{2}+1\right ) y^{\prime }-v \left (v +1\right ) x y = 0
\]
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\[
{} x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 x y = 0
\]
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\[
{} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 \left (n +1\right ) x^{2}+2 n +1\right ) y^{\prime }-\left (v -n \right ) \left (v +n +1\right ) x y = 0
\]
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\[
{} x \left (x^{2}+1\right ) y^{\prime \prime }-\left (2 \left (n -1\right ) x^{2}+2 n -1\right ) y^{\prime }+\left (v +n \right ) \left (-v +n -1\right ) x y = 0
\]
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\[
{} x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3} = 0
\]
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\[
{} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-x y = 0
\]
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✓ |
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\[
{} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+x y = 0
\]
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✓ |
✓ |
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\[
{} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y = 0
\]
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\[
{} x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 x y = 0
\]
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\[
{} x \left (x^{2}-2\right ) y^{\prime \prime }-\left (x^{3}+3 x^{2}-2 x -2\right ) y^{\prime }+\left (x^{2}+4 x +2\right ) y = 0
\]
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\[
{} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right ) y = 0
\]
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\[
{} x^{2} \left (1+x \right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime \prime } = -\frac {2 \left (x -2\right ) y^{\prime }}{x \left (x -1\right )}+\frac {2 \left (1+x \right ) y}{x^{2} \left (x -1\right )}
\]
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\[
{} y^{\prime \prime } = \frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (\left (a +b +1\right ) x +\alpha +\beta -1\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (a b x -\alpha \beta \right ) y}{x^{2} \left (x -1\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {y^{\prime }}{1+x}-\frac {y}{x \left (1+x \right )^{2}}
\]
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\[
{} y^{\prime \prime } = \frac {2 y^{\prime }}{x \left (x -2\right )}-\frac {y}{x^{2} \left (x -2\right )}
\]
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\[
{} y^{\prime \prime } = \frac {2 y}{x \left (x -1\right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +\delta \right )-\delta \right ) x +a \gamma \right ) y^{\prime }}{x \left (x -1\right ) \left (-a +x \right )}-\frac {\left (\alpha \beta x -q \right ) y}{x \left (x -1\right ) \left (-a +x \right )}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (-a +x \right ) \left (x -b \right ) \left (x -c \right )}-\frac {\left (\operatorname {DD} x +E \right ) y}{\left (-a +x \right ) \left (x -b \right ) \left (x -c \right )}
\]
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\[
{} y^{\prime \prime } = \frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )}
\]
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\[
{} y^{\prime \prime } = \frac {y^{\prime }}{1+x}-\frac {\left (3 x +1\right ) y}{4 x^{2} \left (1+x \right )}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}+\frac {v \left (v +1\right ) y}{4 x^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (\left (a +1\right ) x -1\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (\left (a^{2}-b^{2}\right ) x +c^{2}\right ) y}{4 x^{2} \left (x -1\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}-\frac {\left (a x +b \right ) y}{4 x \left (x -1\right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (-3 x +1\right ) y}{\left (x -1\right ) \left (2 x -1\right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (x +a \right ) \left (x +b \right )}-\frac {\left (a -b \right ) y}{4 \left (x +a \right )^{2} \left (x +b \right )}
\]
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\[
{} y^{\prime \prime } = \frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (x -2\right )}+\frac {y}{3 x^{2} \left (x -2\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (a \left (b +2\right ) x^{2}+\left (c -d +1\right ) x \right ) y^{\prime }}{\left (a x +1\right ) x^{2}}-\frac {\left (a b x -c d \right ) y}{\left (a x +1\right ) x^{2}}
\]
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\[
{} y^{\prime \prime } = \frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {a y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (x^{2} a \left (1-a \right )-b \left (x +b \right )\right ) y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left ({\mathrm e}^{\frac {2}{x}}-v^{2}\right ) y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {y^{\prime }}{x^{3}}+\frac {2 y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = \frac {\left (a +b \right ) y^{\prime }}{x^{2}}-\frac {\left (\left (a +b \right ) x +a b \right ) y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (b \,x^{2}+a \left (x^{4}+1\right )\right ) y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {2 y^{\prime }}{x}-\frac {a^{2} y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}+\frac {y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {2 \left (x +a \right ) y^{\prime }}{x^{2}}-\frac {b y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = \frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = \frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {2 y}{x^{4}}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (x^{3}-1\right ) y^{\prime }}{x \left (x^{3}+1\right )}+\frac {x y}{x^{3}+1}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (-v \left (v +1\right ) x^{2}-n^{2}\right ) y}{x^{2} \left (x^{2}+1\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {\left (a \,x^{2}+a -1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (b \,x^{2}+c \right ) y}{x^{2} \left (x^{2}+1\right )}
\]
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\[
{} y^{\prime \prime } = \frac {\left (x^{2}-2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (x^{2}-2\right ) y}{x^{2} \left (x^{2}-1\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}-1}-\frac {v \left (v +1\right ) y}{x^{2} \left (x^{2}-1\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}-1}+\frac {v \left (v +1\right ) y}{x^{2}}
\]
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\[
{} y^{\prime \prime } = \frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (a +1\right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )}
\]
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\[
{} x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-2 x^{3} y^{\prime }-\left (\left (a -n \right ) \left (a +n +1\right ) x^{2} \left (x^{2}-1\right )+2 a \,x^{2}+n \left (n +1\right ) \left (x^{2}-1\right )\right ) y = 0
\]
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\[
{} y^{\prime \prime } = -\frac {\left (a \,x^{2}+a -2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {b y}{x^{2}}
\]
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\[
{} y^{\prime \prime } = \frac {\left (2 b c \,x^{c} \left (x^{2}-1\right )+2 \left (a -1\right ) x^{2}-2 a \right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (b^{2} c^{2} x^{2 c} \left (x^{2}-1\right )+b c \,x^{c +2} \left (2 a -c -1\right )-b c \,x^{c} \left (2 a -c +1\right )+x^{2} \left (a \left (a -1\right )-v \left (v +1\right )\right )-a \left (a +1\right )\right ) y}{x^{2} \left (x^{2}-1\right )}
\]
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\[
{} y^{\prime \prime } = -\frac {a y}{\left (x^{2}+1\right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}+1}-\frac {\left (a^{2} \left (x^{2}+1\right )^{2}-n \left (n +1\right ) \left (x^{2}+1\right )+m^{2}\right ) y}{\left (x^{2}+1\right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {a x y^{\prime }}{x^{2}+1}-\frac {b y}{\left (x^{2}+1\right )^{2}}
\]
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\[
{} y^{\prime \prime } = -\frac {a y}{\left (x^{2}-1\right )^{2}}
\]
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