|
# |
ODE |
Mathematica |
Maple |
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-5 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-9 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+5 x_{2} \left (t \right )-9 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-9 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -17 x_{1} \left (t \right )-42 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+4 x_{2} \left (t \right )-14 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+18 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -16 x_{1} \left (t \right )+30 x_{2} \left (t \right )-18 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+8 x_{2} \left (t \right )+16 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )-15 x_{2} \left (t \right )+9 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )-6 x_{2} \left (t \right )-7 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-3 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+6 x_{2} \left (t \right )+7 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+6 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-5 x_{2} \left (t \right )-6 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+8 x_{2} \left (t \right )+7 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+13 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )+4 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+5 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )+x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-5 x_{2} \left (t \right )+{\mathrm e}^{-t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )-2 x_{2} \left (t \right )+9 t, x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = 10 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+\frac {{\mathrm e}^{6 t}}{t}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{6 t}, x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-9 x_{3} \left (t \right )+1, x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )+t, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+1]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -6 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-7 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 10 x_{1} \left (t \right )-8 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = 8 \,{\mathrm e}^{3 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+3 y = 2 \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+2 y = 4 t
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 6 \cos \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 5 \sin \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 36
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12-6 \,{\mathrm e}^{t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 6 \cos \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 9 \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+2 y = 2 \operatorname {Heaviside}\left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+2 y = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = \operatorname {Heaviside}\left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = \delta \left (t -5\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = \delta \left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+4 y = 3 \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = \delta \left (t -3\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }-2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-2 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+3 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+2 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }-3 x y^{\prime }-5 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
✓ |
✓ |
|