| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{3}-x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } \left (1+x \right )+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } \cos \left (x \right )+y^{\prime } \sin \left (x \right )-2 \cos \left (x \right )^{3} y = 2 \cos \left (x \right )^{5}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y-x^{2} y^{\prime }+y^{\prime \prime } = x^{1+m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 b x y^{\prime }+y b^{2} x^{2} = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\sqrt {x}\, y^{\prime }+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y \,{\mathrm e}^{2 x}-{\mathrm e}^{3 x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }-x y-{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-x y^{\prime }-y-x \left (1+x \right ) {\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y-x^{2} a = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-v^{2}+x^{2}\right ) y-f \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y-3 x^{3} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (x^{2} a +12 a +4\right ) \cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (-v^{2}+x^{2}+1\right ) y-f \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-x^{2} \ln \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-x^{3} \sin \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {d}{d x}\operatorname {LegendreP}\left (n , x\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2 = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (\ln \left (x \right )^{2} x^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+x y-1 = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = -\frac {\left (2 a x +b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (a v x -b \right ) y}{\left (a x +b \right ) x^{2}}+A x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {b y}{x^{2} \left (x -a \right )^{2}}+c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y = c \,x^{2} \left (x -a \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+x \right )^{2} y^{\prime \prime }-y^{\prime } \left (1+x \right )+6 y = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y-x^{2} y^{\prime }+y^{\prime \prime } = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 \sin \left (x \right ) y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -x y+2 y^{\prime }+x y^{\prime \prime } = 2 \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+y \,{\mathrm e}^{2 x} = {\mathrm e}^{4 x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime } = \frac {1}{x^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 4 x^{3} {\mathrm e}^{-x^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1+x \right ) y-2 x \left (1+x \right ) y^{\prime }+x^{2} y^{\prime \prime } = x^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+x y^{\prime } = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y = \cos \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime }+t x^{\prime \prime } = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \frac {x^{\prime }+t x^{\prime \prime }}{t} = -2
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }-2 x = t^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{\prime \prime }+\frac {x^{\prime }}{t} = a
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1+x \right )^{2} y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+2 y = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+2 y = \left (x +2\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 y = 4 x -8
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-6 y = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }-2 x = t^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )+y = 2 \cos \left (\ln \left (1+x \right )\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|