| # | ODE | Mathematica | Maple | Sympy |
| \[
{} -y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime } = \cot \left (x \right )
\]
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✓ |
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| \[
{} \sin \left (x \right ) y-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = \ln \left (x \right )
\]
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✓ |
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| \[
{} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
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✗ |
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| \[
{} f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
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| \[
{} 4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0
\]
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| \[
{} -3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime } = 0
\]
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✓ |
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| \[
{} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime \prime } = 2
\]
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| \[
{} x y+3 y^{\prime }+x y^{\prime \prime \prime } = 0
\]
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| \[
{} -y+x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = 0
\]
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| \[
{} y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = 0
\]
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| \[
{} y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = -x^{2}+1
\]
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| \[
{} -x^{2} y+3 y^{\prime \prime }+x y^{\prime \prime \prime } = 0
\]
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✓ |
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| \[
{} 2 y+4 x y^{\prime }-\left (-x^{2}+3\right ) y^{\prime \prime }+x y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -2 y^{\prime }-\left (x +4\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime \prime \prime } = 0
\]
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| \[
{} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime } = 0
\]
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✓ |
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| \[
{} 2 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = a
\]
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| \[
{} 3 x y+y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = f \left (x \right )
\]
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✓ |
✓ |
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| \[
{} 4 y^{\prime }+5 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = \ln \left (x \right )
\]
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✓ |
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| \[
{} 6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
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✓ |
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✓ |
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| \[
{} a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} 6 n y^{\prime }-2 \left (n +1\right ) x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
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| \[
{} 10 y^{\prime }+8 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
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| \[
{} -2 x y+y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime }+\left (x +2\right ) y^{\prime \prime }+\left (x +2\right )^{2} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y+x y^{\prime }+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime } = f \left (x \right )
\]
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✓ |
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| \[
{} x^{3} y^{\prime \prime \prime } = a
\]
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✓ |
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| \[
{} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
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| \[
{} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime } = x \ln \left (x \right )
\]
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✓ |
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✓ |
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| \[
{} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = x \left (x^{2}+3\right )
\]
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✓ |
✓ |
✓ |
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| \[
{} -8 y+3 x y^{\prime }+x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = a
\]
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✓ |
✓ |
✓ |
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| \[
{} 2 y-2 x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 8 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -\left (-a \,x^{3}+12\right ) y+6 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -y+2 x y^{\prime }+x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 2 x^{3}
\]
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✓ |
✓ |
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| \[
{} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -4 y-14 x y^{\prime }+\left (-8 x^{2}+3\right ) y^{\prime \prime }+x \left (-x^{2}+1\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} \left (-x^{3}+3 x^{2}-6 x +6\right ) y^{\prime \prime }+x \left (x^{2}-2 x +2\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -8 y+3 y^{\prime } \left (1+x \right )+\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right )^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -y+x y^{\prime }+4 x^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 2 y+\left (1-2 x \right ) y^{\prime }+\left (1-2 x \right )^{3} y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 x y+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime } = 10 x^{2}+10
\]
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✓ |
✓ |
✓ |
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| \[
{} x y-x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime } = 1
\]
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✓ |
✓ |
✓ |
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| \[
{} 10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime } = -1+3 x^{2}+2 x^{2} \ln \left (x \right )
\]
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✓ |
✓ |
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| \[
{} -4 \left (3 x +1\right ) y+2 x \left (5 x +2\right ) y^{\prime }-2 x^{2} \left (2 x +1\right ) y^{\prime \prime }+x^{3} \left (1+x \right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime } = 1
\]
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✓ |
✓ |
✓ |
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| \[
{} -4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (a -x \right )^{3} \left (-x +b \right )^{3} y^{\prime \prime \prime } = c y
\]
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✓ |
✓ |
✗ |
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| \[
{} \sin \left (x \right )-y \cos \left (x \right )-3 y^{\prime } \sin \left (x \right )+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }+\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime \prime \prime } = 0
\]
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✓ |
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✓ |
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| \[
{} y^{\prime \prime \prime \prime } = x \cos \left (x \right )
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 \,{\mathrm e}^{-x} \cos \left (x \right )+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime \prime \prime } = y+\cos \left (x \right )
\]
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✓ |
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✓ |
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| \[
{} y^{\prime \prime \prime \prime } = {\mathrm e}^{x} \cos \left (x \right )+y
\]
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✓ |
✓ |
✓ |
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| \[
{} a y+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
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| \[
{} y^{\prime \prime \prime \prime } = x^{3}+a^{4} y
\]
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✓ |
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✓ |
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| \[
{} y+y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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| \[
{} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
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✓ |
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| \[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = 0
\]
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✓ |
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✓ |
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| \[
{} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = \cos \left (x \right )
\]
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| \[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right )
\]
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✓ |
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| \[
{} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 24 x \sin \left (x \right )
\]
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✓ |
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| \[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = 4+{\mathrm e}^{x}
\]
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✓ |
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✓ |
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| \[
{} -8 y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
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✓ |
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| \[
{} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0
\]
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✓ |
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| \[
{} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0
\]
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✓ |
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✓ |
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| \[
{} 27 y-12 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
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✓ |
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| \[
{} a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
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✓ |
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| \[
{} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime } = \cosh \left (a x \right )
\]
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✓ |
✓ |
✓ |
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| \[
{} y a^{2} b^{2}+\left (a^{2}+b^{2}\right ) y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = {\mathrm e}^{3 x}
\]
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✓ |
✓ |
✓ |
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| \[
{} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -y^{\prime }+y^{\prime \prime }-3 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 16 y-16 y^{\prime }+12 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 y a^{2} b^{2}+2 \left (a^{2}+b^{2}\right ) y^{\prime \prime }+2 y^{\prime \prime \prime \prime } = \cos \left (a x \right )+\cos \left (b x \right )
\]
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✓ |
✓ |
✓ |
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| \[
{} -3 y^{\prime }+11 y^{\prime \prime }-12 y^{\prime \prime \prime }+4 y^{\prime \prime \prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 3 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } x = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 5 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } x = 0
\]
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✓ |
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✓ |
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| \[
{} x^{2} y^{\prime \prime \prime \prime } = 2 y^{\prime \prime \prime }
\]
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✓ |
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✓ |
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| \[
{} x^{2} y^{\prime \prime \prime \prime } = 2 y^{\prime \prime }
\]
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✓ |
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✓ |
|