|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} \left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (5+x \right ) y^{\prime }+10 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 5 x y^{\prime \prime }+8 y^{\prime }-x y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+2 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-k^{2}+x^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+k \left (k +1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 3 x y^{\prime \prime }+11 y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (1+x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 1-x y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {y-x}{x +y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-\sin \left (x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+y \sin \left (x \right ) = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\]
|
✗ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime \prime }+x \sin \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-2 x y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-x y^{\prime }+y = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-\left (x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } = x^{2} y-y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = {\mathrm e}^{y}+x y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (1+x \right ) y^{\prime }-n y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 x y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+y = 1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime } = y
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime } = y
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = 1+y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = x -y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y^{\prime }-x y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+n^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 x y^{\prime }+2 n y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} \left (3 x +1\right ) x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y \sin \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+y \sin \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+y \sin \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime }+y \sin \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime }+y \sin \left (x \right ) = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}} = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (1-x \right ) y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\]
|
✓ |
✗ |
✓ |
|
|
\[
{} \left (-x^{2}+x \right ) y^{\prime \prime }+4 y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{4} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x}
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (2 x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|