|
# |
ODE |
Mathematica |
Maple |
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }-2 x y = x^{4}+12
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y}{\ln \left (x \right ) x^{2}} = {\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime } \sin \left (x \right )^{2}+\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = \left (1+x \right ) {\mathrm e}^{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = \frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y = 4 x^{2} {\mathrm e}^{x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right ) \sin \left (2 x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3}+3 x
\] |
✓ |
✓ |
|
|
\[
{}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1-\frac {m^{2}}{x^{2}}\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-x^{3} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\] |
✗ |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y^{\prime }\left (x \right ) = y \left (x \right )+z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )+z \left (x \right )+x]
\] |
✓ |
✓ |
|
|
\[
{}\left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {y \left (x \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [y^{\prime }\left (x \right ) = 1-\frac {1}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {1}{y \left (x \right )-x}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[y^{\prime }\left (x \right ) = -z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )]
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime } = y^{2}+x
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
\] |
✗ |
✗ |
|
|
\[
{}\left [y^{\prime }\left (x \right ) = \frac {z \left (x \right )^{2}}{y \left (x \right )}, z^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {z \left (x \right )^{2}}{y \left (x \right )}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = t^{2}, y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = 2 t, z^{\prime }\left (t \right )+z \left (t \right ) = t]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = 7 \,{\mathrm e}^{t}-27, y^{\prime }\left (t \right )-2 x \left (t \right )+3 y \left (t \right ) = -3 \,{\mathrm e}^{t}+12]
\] |
✓ |
✓ |
|
|
\[
{}[y^{\prime \prime }\left (x \right )+z^{\prime }\left (x \right )-2 z \left (x \right ) = {\mathrm e}^{2 x}, z^{\prime }\left (x \right )+2 y^{\prime }\left (x \right )-3 y \left (x \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+{\mathrm e}^{t}+{\mathrm e}^{-t}]
\] |
✓ |
✓ |
|
|
\[
{}\left [y^{\prime }\left (x \right )+\frac {2 z \left (x \right )}{x^{2}} = 1, z^{\prime }\left (x \right )+y \left (x \right ) = x\right ]
\] |
✓ |
✓ |
|
|
\[
{}[t x^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = t, t y^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}[t x^{\prime }\left (t \right )+6 x \left (t \right )-y \left (t \right )-3 z \left (t \right ) = 0, t y^{\prime }\left (t \right )+23 x \left (t \right )-6 y \left (t \right )-9 z \left (t \right ) = 0, t z^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )-2 z \left (t \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )+3 y \left (t \right )-x \left (t \right ) = {\mathrm e}^{2 t}]
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 2 x
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = 2 y
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{2 x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = k y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = y+x^{2}+y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{4} {y^{\prime }}^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
✓ |
✓ |
|
|
\[
{}1+y^{2}+y^{\prime } y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}-x
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = 1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\left (1+x \right ) y^{\prime } = x
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}x y y^{\prime } = y-1
\] |
✓ |
✓ |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = \left (-2 x^{2}+1\right ) \tan \left (y\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y \ln \left (y\right )-x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \ln \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = 1
\] |
✓ |
✓ |
|
|
\[
{}x \left (x^{2}-4\right ) y^{\prime } = 1
\] |
✓ |
✓ |
|
|
\[
{}\left (1+x \right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x -2 y}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = 2 x^{2}+1
\] |
✓ |
✓ |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}x y y^{\prime } = \left (1+x \right ) \left (1+y\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 2 x y+1
\] |
✓ |
✓ |
|