|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} \left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-2 y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 {y^{\prime }}^{2} x = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime \prime } = 2 x y-{\mathrm e}^{y}-x
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } = 2 {y^{\prime }}^{3} y
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-y^{\prime } = 3 x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime }+y^{\prime } x^{2}+x y = 1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+3 y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }+x^{3} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+3 x y^{\prime }+x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (1+x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime } = 17 x^{6}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x = \cos \left (3 \ln \left (t \right )\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime } = x y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{3} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = r y^{\prime \prime }
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 x y y^{\prime }+3 x^{2} y^{2}\right ) y^{\prime }+y^{3} x^{3} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} v^{\prime \prime \prime }+2 x^{2} v^{\prime \prime }+v = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime } = 2 x
\]
|
✓ |
✓ |
✓ |
|