|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1+x \right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x y^{\prime } = y
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } x^{2}+y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime } = 2 y
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+y^{\prime } x^{2}+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{x +{\mathrm e}^{y}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = -\frac {4 x +3 y}{y+2 x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {3 y+x}{x -y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = t -1-y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {-a x +b y}{b x -c y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 x -2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+{\mathrm e}^{x y} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{x y} x \cos \left (2 x \right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \ln \left (x \right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} -1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {y+2 x}{3-x +3 y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {-1-2 x y-y^{2}}{x^{2}+2 x y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {-1-2 x y}{x^{2}+2 y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2}+y+\left (x +{\mathrm e}^{y}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {-4+6 x y+2 y^{2}}{3 x^{2}+4 x y+3 y^{2}}+y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x^{2}-1}{1+y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 x y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 y^{\prime \prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y^{\prime \prime }+3 y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right ) {\mathrm e}^{-t}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-t y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} t^{2} \left (3+t \right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right .
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right .
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right .
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-2 y = -1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }+\frac {\left (1+y\right ) \left (-1+y\right ) \left (-2+y\right )}{1+x} = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = 2 x y \left (1+y^{2}\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }+y = \frac {2 x \,{\mathrm e}^{-x}}{1+y \,{\mathrm e}^{x}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-y = \frac {\left (1+x \right ) {\mathrm e}^{4 x}}{\left (y+{\mathrm e}^{x}\right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-2 y = \frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x^{2}+y^{2}}{\sin \left (x \right )}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \frac {y+{\mathrm e}^{x}}{x^{2}+y^{2}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \tan \left (x y\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x^{2}+y^{2}}{\ln \left (x y\right )}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \left (x^{2}+y^{2}\right ) y^{{1}/{3}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \ln \left (1+x^{2}+y^{2}\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \sqrt {x^{2}+y^{2}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \left (x^{2}+y^{2}\right )^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = y^{{2}/{5}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = 3 x \left (-1+y\right )^{{1}/{3}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = 3 x \left (-1+y\right )^{{1}/{3}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 7 x y^{\prime }-2 y = -\frac {x^{2}}{y^{6}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-x y = x y^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-y = x \sqrt {y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {y}{y-2 x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y y^{\prime } = x^{2}-x y+y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {2 y^{2}-x y+2 x^{2}}{x y+2 x^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x^{2}+x y+y^{2}}{x y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {2 x +y+1}{x +2 y-4}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {y^{2}+y \tan \left (x \right )+\tan \left (x \right )^{2}}{\sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \ln \left (x \right )^{2} y^{\prime } = -4 \ln \left (x \right )^{2}+y \ln \left (x \right )+y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (y+{\mathrm e}^{x^{2}}\right ) y^{\prime } = 2 x \left (y^{2}+y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x^{2}}\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 \cos \left (x \right ) y+4 \,{\mathrm e}^{x} x +2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x -2 y^{2}+\left (12 y^{2}-4 x y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} -2 \sin \left (x \right ) y^{2}+3 y^{3}-2 x +\left (4 \cos \left (x \right ) y+9 x y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 x^{2}+2 x y+4 y^{2}+\left (x^{2}+8 x y+18 y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x^{2}+8 x y+y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|