|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{\prime } = x^{2} y^{2}-4 x^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = 2 \sqrt {y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x y+\left (x^{2}+3 y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = y y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\sin \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\sin \left (y\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+x y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right ) x -y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right )]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }+x y = y^{4} x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y-x^{3}+\left (y^{3}+x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x y^{3}+\cos \left (x \right ) y+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime } = \sqrt {x^{2}+y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x +y-1}{x +4 y+2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y+\left (x -2 x^{2} y^{3}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y \ln \left (y\right )-2 x y+\left (x +y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2}+x y+1+\left (x^{2}+x y+1\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x^{2}+y^{2}}{-y^{2}+x^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }+y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (1+x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\sin \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime } = y
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } x^{2} = y
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{\prime }-\frac {y}{x} = x^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 x y^{\prime }-y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+y^{\prime }-x^{2} y = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime }+y \sin \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime }+y \sin \left (x \right ) = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime }-4 y^{\prime } x^{2}+3 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} \left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 x y = x^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-x y^{\prime }+y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+y^{\prime }+y = x^{3}-x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x^{2}+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+z \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 1+t y \left (t \right ), y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = -x +y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = y+x \,{\mathrm e}^{y}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-x y = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-4 x y^{\prime }-4 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+5 x y^{\prime }+y \sqrt {x} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime }+4 y^{\prime } x^{2}+3 y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime }+y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+y^{\prime } x^{2}+2 x y = 10 x^{3}-2 x +5
\]
|
✓ |
✓ |
✗ |
|