|
# |
ODE |
Mathematica |
Maple |
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
✓ |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+3 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+3 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 1
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+6 y = {\mathrm e}^{4 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (5 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{t}
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-3 t} \cos \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-4 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 1+t \,{\mathrm e}^{t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = t +1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+20 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = t \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = t \,{\mathrm e}^{t} \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (3 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}t y^{\prime \prime }-y^{\prime } = 2 t^{2}
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-3 y = \delta \left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+8 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )-9 z \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 10 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right )+t -1, y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right )-3 t^{2}, z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )+t^{2}-t +2]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ), z^{\prime }\left (t \right ) = y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{5 t}, z^{\prime }\left (t \right ) = -2 y \left (t \right )+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t, z^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t]
\] |
✓ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-7 y \left (t \right )+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right )}{4}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )-z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )-z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-2 y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 10 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-12 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -6 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|