| # | ODE | Mathematica | Maple | Sympy |
| \[
{} -a \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} b \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} 2 y-\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} k \left (1+k \right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (p \left (p +1\right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a0} -\operatorname {a2} \csc \left (x \right )^{2}+4 \operatorname {a1} \sin \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} 3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} 3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \csc \left (x \right )
\]
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| \[
{} \left (b +k^{2} \cos \left (x \right )^{2}\right ) y+a \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (a \cot \left (x \right )^{2}+b \cot \left (x \right ) \csc \left (x \right )+c \csc \left (x \right )^{2}\right ) y+k \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} 2 y-\cot \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} a \tan \left (x \right )^{2} y-2 \cot \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} c y+a \cot \left (b x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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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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| \[
{} \left (\cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime }+y^{\prime \prime } = 1+a \csc \left (x \right )
\]
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| \[
{} \csc \left (x \right )^{2} \left (2+\sin \left (x \right )^{2}\right ) y-\csc \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} a \csc \left (x \right )^{2} y+\left (2+\cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -2 \left (\cos \left (x \right )+1\right ) \sec \left (x \right ) y-\left (2+3 \cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \sin \left (x \right )^{2} y-\left (\cot \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -y \cos \left (x \right )-y^{\prime } \sin \left (x \right )+y^{\prime \prime } = a -x +x \ln \left (x \right )
\]
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| \[
{} b \tan \left (x \right )^{2} y-2 \csc \left (2 x \right ) \left (1-a \sin \left (x \right )^{2}\right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} a \cot \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -a \left (a +1\right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (a \cos \left (x \right )^{2}-\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = \left (1+x \right ) \sec \left (x \right )
\]
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| \[
{} 3 y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} b y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = \sin \left (x \right )
\]
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| \[
{} b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} y \,{\mathrm e}^{2 x}-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a0} -\operatorname {a2} \operatorname {csch}\left (x \right )^{2}+4 \operatorname {a1} \sinh \left (x \right )^{2}\right ) y+\coth \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a0} +4 \operatorname {a1} \cosh \left (x \right )^{2}-\operatorname {a2} \operatorname {sech}\left (x \right )^{2}\right ) y+\tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} b y+2 \tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} b y+a \tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} f \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} a k \,x^{k -1} y+2 a \,x^{k} y^{\prime }+2 y^{\prime \prime } = 0
\]
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| \[
{} 3 y-10 y^{\prime }+3 y^{\prime \prime } = 0
\]
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| \[
{} 4 y^{\prime \prime } = \left (x^{2}+a \right ) y
\]
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| \[
{} \left (-x^{2}+4 a +2\right ) y+4 y^{\prime \prime } = 0
\]
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| \[
{} 3 y-8 y^{\prime }+4 y^{\prime \prime } = 0
\]
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| \[
{} y+x y^{\prime \prime } = 0
\]
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| \[
{} \left (x +a \right ) y+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = x^{n}
\]
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| \[
{} -y+y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -\left (1+x \right ) y+y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
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| \[
{} -a^{2} x^{3} y-y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -x y+2 y^{\prime }+x y^{\prime \prime } = {\mathrm e}^{x}
\]
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| \[
{} a x y+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} a \,x^{2} y+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y+\left (1-a \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -y+2 n y^{\prime }+x y^{\prime \prime } = 0
\]
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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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| \[
{} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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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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| \[
{} b \,x^{k} y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = 0
\]
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| \[
{} n y+\left (1-x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} n y+\left (1+k -x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 2 \left (1-x \right ) y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = 0
\]
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| \[
{} -y-\left (2-x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 3 y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} b y+\left (x +a \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -a y+\left (c -x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -\left (1-x \right ) y+\left (1-2 x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1
\]
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| \[
{} c y+\left (b x +a \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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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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| \[
{} -y^{\prime } \left (-x^{2}+1\right )+x y^{\prime \prime } = 0
\]
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| \[
{} 2 x y-\left (-x^{2}+4\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 4 x^{3} {\mathrm e}^{-x^{2}}
\]
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| \[
{} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} a \,x^{2} \left (a \,x^{3}+1\right ) y-\left (-2 a \,x^{3}+1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = 0
\]
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2}
\]
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| \[
{} 3 \left (2-x \right ) y-\left (9-4 x \right ) y^{\prime }+\left (3-x \right ) y^{\prime \prime } = 0
\]
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| \[
{} -2 y^{\prime }+\left (a -x \right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (x +a \right ) y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime }+2 x y^{\prime \prime } = 0
\]
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| \[
{} a y+y^{\prime }+2 x y^{\prime \prime } = 0
\]
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