| # | ODE | Mathematica | Maple | Sympy |
| \[
{} -{y^{\prime }}^{2}+4 {y^{\prime }}^{3} y+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{2} \left (1-b^{2} {y^{\prime }}^{2}\right )+2 b^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2}-b^{2} y^{2}\right ) {y^{\prime \prime }}^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2} = 4 x y \left (x y^{\prime }-y\right )^{3}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} f \left (y^{\prime \prime }\right )+x y^{\prime \prime } = y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} f \left (\frac {y^{\prime \prime }}{y^{\prime }}\right ) y^{\prime } = {y^{\prime }}^{2}-y y^{\prime \prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} f \left (y^{\prime \prime }, y^{\prime }-x y^{\prime \prime }, y-x y^{\prime }+\frac {x^{2} y^{\prime \prime }}{2}\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime } = x y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+2 x y^{\prime }+y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y+2 a x y^{\prime }+y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} f^{\prime }\left (x \right ) y+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 x y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime } = \cot \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right ) y-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = \ln \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime \prime } = 2
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y+3 y^{\prime }+x y^{\prime \prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -y+x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = -x^{2}+1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -x^{2} y+3 y^{\prime \prime }+x y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y+4 x y^{\prime }-\left (-x^{2}+3\right ) y^{\prime \prime }+x y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 y^{\prime }-\left (x +4\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = a
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x y+y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = f \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 y^{\prime }+5 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 6 n y^{\prime }-2 \left (n +1\right ) x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 10 y^{\prime }+8 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -2 x y+y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+\left (x +2\right ) y^{\prime \prime }+\left (x +2\right )^{2} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+x y^{\prime }+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime } = f \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime \prime } = a
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime } = x \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = x \left (x^{2}+3\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -8 y+3 x y^{\prime }+x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = a
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y-2 x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 8 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (-a \,x^{3}+12\right ) y+6 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+2 x y^{\prime }+x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 2 x^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -4 y-14 x y^{\prime }+\left (-8 x^{2}+3\right ) y^{\prime \prime }+x \left (-x^{2}+1\right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{3}+3 x^{2}-6 x +6\right ) y^{\prime \prime }+x \left (x^{2}-2 x +2\right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -8 y+3 y^{\prime } \left (1+x \right )+\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right )^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -6 y+6 y^{\prime } \left (1+x \right )-3 x \left (x +2\right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -y+x y^{\prime }+4 x^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y+\left (1-2 x \right ) y^{\prime }+\left (1-2 x \right )^{3} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x y+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime } = 10 x^{2}+10
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y-x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime } = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime } = -1+3 x^{2}+2 x^{2} \ln \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -4 \left (3 x +1\right ) y+2 x \left (5 x +2\right ) y^{\prime }-2 x^{2} \left (2 x +1\right ) y^{\prime \prime }+x^{3} \left (1+x \right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime } = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a -x \right )^{3} \left (-x +b \right )^{3} y^{\prime \prime \prime } = c y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right )-y \cos \left (x \right )-3 y^{\prime } \sin \left (x \right )+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }+\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = x^{3}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 5 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime \prime \prime } = 2 y^{\prime \prime \prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime \prime \prime } = 2 y^{\prime \prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 6 y^{\prime \prime }+6 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x +a \right )^{2} y^{\prime \prime \prime \prime } = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -c^{4} y+16 \left (1+a -b \right ) \left (2+a -b \right ) y^{\prime \prime }+32 \left (2+a -b \right ) x y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -a^{4} x^{3} y-x y^{\prime \prime }+2 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 6 x y^{\prime \prime }+6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -k y-\left (-a b c +x \right ) y^{\prime }+\left (a b +a c +b c +a +b +c +1\right ) x y^{\prime \prime }+\left (3+a +b +c \right ) x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -4 y-2 x y^{\prime }+4 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -b^{4} x^{\frac {2}{a}} y+16 \left (-2 a +1\right ) \left (1-a \right ) a^{2} x^{2} y^{\prime \prime }-32 \left (-2 a +1\right ) a^{2} x^{3} y^{\prime \prime \prime }+16 a^{4} x^{4} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y \,{\mathrm e}^{x}+4 \,{\mathrm e}^{x} y^{\prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime } = y^{\prime } \left (1+y^{\prime }\right )
\]
|
✗ |
✓ |
✗ |
|