| # | ODE | Mathematica | Maple | Sympy |
| \[
{} -6 x y+2 y^{\prime }+x \left (3 x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} \left (3 x +1\right ) y-4 x^{2} y^{\prime }+4 x^{2} \left (1+x \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
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| \[
{} 2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} \left (b x +a \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime } = 0
\]
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✗ |
✗ |
✗ |
|
| \[
{} a^{2} y+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (-2 x^{2}+1\right ) y+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -\left (2 x^{2}+1\right ) y+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (-a^{2}+{\mathrm e}^{\frac {2}{x}}\right ) y+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -2 y+x y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (2 x +1\right ) y-2 x^{2} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -\left (1+x \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (c \,x^{4}+b \,x^{2}+a \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} y+x \left (x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-x^{2}+1\right ) y-x \left (-x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} a^{2} y+2 x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
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| \[
{} -y+x \left (2 x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+2 x^{2} \left (x +a \right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -x^{2} y-\left (-x^{3}+1\right ) y^{\prime }+x \left (x^{3}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 y-x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+2\right ) y-x \left (-x^{2}+2\right ) y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} a \left (a +1\right ) y-2 x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -a^{2} y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -\left (m^{2}-n \left (n +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (k^{2}-p \left (p +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (a^{2}-k \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y b^{2}+x \left (a^{2}+2 x^{2}\right ) y^{\prime }+x^{2} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -2 \left (1-x \right ) y+2 \left (3-x \right ) x \left (1+x \right ) y^{\prime }+\left (1-x \right ) x \left (1+x \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+\left (1-2 x \right ) \left (1-x \right ) x y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (1-x \right ) x \left (\operatorname {b2} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = k^{2} y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} B y+\left (a -x \right ) \left (-x +b \right ) \left (A +2 x \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y-2 \left (a -x \right )^{3} y^{\prime }+\left (a -x \right )^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 \left (3 x +1\right ) y+2 \left (2-3 x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-x \right ) y+2 \left (1-2 x \right ) \left (2-x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (4 k^{2}+\left (4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (4 k^{2}+\left (-4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (a \left (a +1\right ) \left (1-x \right )+b^{2} x \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) x y^{\prime }+4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y+\left (b x +a \right )^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} A y+\left (c \,x^{2}+b x +a \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+x y^{\prime }+x^{5} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-2 x^{3}+1\right ) y-x \left (-2 x^{3}+1\right ) y^{\prime }+x^{5} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+\left (\operatorname {b0} \,x^{4}+\operatorname {a0} \right ) y^{\prime }+x \left (a^{2}-x^{2}\right ) \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (-x +b \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} \left (c -x \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-2 x^{2}+1\right ) y+4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (8 x^{4}+10 x^{2}+1\right ) y-4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1-a \right )^{2} y+a \,x^{2 a -1} y^{\prime }+x^{2 a} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a^{2} x^{a -1} y+\left (-2 a +1\right ) x^{a} y^{\prime }+x^{a +1} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {a2} +\operatorname {b2} \,x^{k}\right ) y+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) y^{\prime }+x^{2} \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}\right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -\left (4 k^{2}-\left (-p^{2}+1\right ) \sinh \left (x \right )^{2}\right ) y+4 \cosh \left (x \right ) \sinh \left (x \right ) y^{\prime }+4 \sinh \left (x \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = a y
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 6 y^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 2 y^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a \,x^{r} y^{s}+y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a \sin \left (y\right )+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \,{\mathrm e}^{y}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = f \left (y\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+3 f \left (x \right ) y^{\prime }+y^{\prime \prime } = 2 y^{3}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+y y^{\prime } = y^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y+y y^{\prime }+y^{\prime \prime } = y^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 a^{2} y+a y^{2}+\left (3 a +y\right ) y^{\prime }+y^{\prime \prime } = y^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = f \left (x \right ) y^{2}+y^{3}+y \left (-2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+\left (3 f \left (x \right )-y\right ) y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = f^{\prime }\left (x \right ) y+\left (f \left (x \right )-2 y\right ) y^{\prime }
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = f \left (x \right ) y^{2}-y^{3}+\left (f \left (x \right )-3 y\right ) y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a \left (1+2 y y^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a \left (y^{2}-1\right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 \cot \left (x \right ) y^{\prime }+2 \tan \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} b y+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} f \left (x \right ) y^{\prime }+g \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} b y+a y {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} g \left (y\right )+f \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} f \left (x \right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} h \left (y\right )+f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = \left (a -x \right ) {y^{\prime }}^{3}
\]
|
✓ |
✓ |
✓ |
|