| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\left (t +1\right ) x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\cos \left (t \right ) t -\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }-x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cot \left (x \right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{1+x}-\frac {\left (x +2\right ) y}{x^{2} \left (1+x \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+x^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✗ |
✗ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime } = 2 y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime } = 2 y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x^{2} y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+x^{2} y^{\prime } = 4 y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1+x \right )^{2} y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y = 0
\]
|
✓ |
✓ |
✓ |
|