|
# |
ODE |
Mathematica |
Maple |
|
\[
{}[x^{\prime }\left (t \right )+5 x \left (t \right )-2 y \left (t \right ) = 0, y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right ) = 0, y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+x \left (t \right )-z \left (t \right ) = 0, y^{\prime }\left (t \right )-y \left (t \right )+x \left (t \right ) = 0, z^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right )-3 z \left (t \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}+2 y \left (t \right )-3 z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-\frac {z \left (t \right )}{2}, z^{\prime }\left (t \right ) = -2 x \left (t \right )+z \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = y \left (t \right ), x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right ) = t, x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-t, 2 x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right ) = 2 x \left (t \right )+6]
\] |
✓ |
✓ |
|
|
\[
{}[2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = t, 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right ) = y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[5 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), 3 x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = t]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right ) = 0, 2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right ) = y \left (t \right )+t]
\] |
✓ |
✓ |
|
|
\[
{}[3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+t]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+9 y \left (t \right )+12 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = -5 x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+6 y \left (t \right )+6 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = -12 x \left (t \right )+5 y \left (t \right )+37]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+10 y \left (t \right )+18 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -10 x \left (t \right )+9 y \left (t \right )+37]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -14 x \left (t \right )+39 y \left (t \right )+78 \sinh \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )+16 y \left (t \right )+6 \cosh \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right )-2 \sinh \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+10 \cosh \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right )-2 z \left (t \right )+50 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 6 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+21 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = -x \left (t \right )+6 y \left (t \right )+z \left (t \right )+9]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-2 y \left (t \right )+6 z \left (t \right )+{\mathrm e}^{2 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+2 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = -2 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )-1-6 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )+4 \,{\mathrm e}^{t}-3]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+24 \sin \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )+12 \cos \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right )+10 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 3 x \left (t \right )+14 y \left (t \right )+6 \,{\mathrm e}^{2 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+4 y \left (t \right )+6 \,{\mathrm e}^{3 t}, y^{\prime }\left (t \right ) = -5 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right )+5 \sin \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right )-10 \cos \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right )+2]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \sin \left (2 t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right )-3 z \left (t \right )+5 \cos \left (2 t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )+7 y \left (t \right )+3 z \left (t \right )+23 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right )-3 z \left (t \right )+2 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+2 z \left (t \right )+4 \,{\mathrm e}^{t}, z^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right )+4 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+5 y \left (t \right )+10 \sinh \left (t \right ), y^{\prime }\left (t \right ) = 19 x \left (t \right )-13 y \left (t \right )+24 \sinh \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )-6 t, y^{\prime }\left (t \right ) = -x \left (t \right )+11 y \left (t \right )+10 t]
\] |
✓ |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{{3}/{2}} {\mathrm e}^{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \sec \left (2 x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = f \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }-k y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
✓ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\alpha ^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-\alpha ^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\beta y^{\prime }+\gamma y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime }-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y \left (1-{y^{\prime }}^{2}\right ) = \left (-y^{2}-a^{2}+x^{2}\right ) y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}1+y-\left (1-x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y-a +x^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
✓ |
✓ |
|
|
\[
{}1+s^{2}-\sqrt {t}\, s^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x +y+x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x +y+\left (y-x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 \sqrt {s t}-s+t s^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}t -s+t s^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2} y^{\prime } x = y^{3}+x^{3}
\] |
✓ |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )
\] |
✓ |
✓ |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x +2 y+1-\left (4 y+2 x +3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {-x y^{\prime }+y}{\sqrt {x^{2}+y^{2}}} = m
\] |
✓ |
✓ |
|
|
\[
{}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\] |
✓ |
✓ |
|
|
\[
{}y+\frac {x}{y^{\prime }} = \sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {a y}{x} = \frac {1+x}{x}
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1
\] |
✓ |
✓ |
|
|
\[
{}s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {n y}{x} = {\mathrm e}^{x} x^{n}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1 = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
✓ |
✓ |
|