|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t y^{\prime \prime }+t y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} z y^{\prime \prime }-2 y^{\prime }+y z = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 y^{\prime \prime }+x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 x y^{\prime \prime }-x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (-x +4\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (-x +4\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (1+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (1+x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 x y}{16} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} \left (2-x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (1+x \right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-x y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|