|
# |
ODE |
Mathematica |
Maple |
|
\[
{}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 3 x^{{3}/{2}} \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = g \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2}
\] |
✓ |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2}
\] |
✓ |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = g \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }-y = t^{2} {\mathrm e}^{2 t}
\] |
✓ |
✓ |
|
|
\[
{}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = t^{2} {\mathrm e}^{t}+7
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = t^{2}+7
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = t \cos \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y = t \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = t
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+25 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+29 y = {\mathrm e}^{-2 t} \sin \left (5 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+w^{2} y = \cos \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = \cos \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 18 \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-9 y = 0
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -5 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -9 y_{1} \left (t \right )+5 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 6 y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-4 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 6 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-64 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-14 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )-y_{2} \left (t \right )+2 \,{\mathrm e}^{t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )+\sin \left (2 t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-y_{2} \left (t \right )+{\mathrm e}^{-t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+3 y_{2} \left (t \right )+2 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-5 y_{2} \left (t \right )+3, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+3 y_{2} \left (t \right )+5 \cos \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )+\sin \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{3} \left (t \right )-{\mathrm e}^{-t}, y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right )+{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \operatorname {Heaviside}\left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -3 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
✓ |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2}
\] |
✓ |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = 2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = -20 \delta \left (t -3\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -4 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }+6 y = \delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{5}+y = k \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{10}+y = k \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+w^{2} y = g \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = \sin \left (\alpha t \right )
\] |
✓ |
✓ |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+17 y = g \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = g \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = g \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = g \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}\frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}\frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y = t
\] |
✓ |
✓ |
|
|
\[
{}t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right )
\] |
✗ |
✗ |
|
|
\[
{}t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y = \ln \left (t \right )
\] |
✗ |
✗ |
|
|
\[
{}\left (x -4\right ) y^{\prime \prime \prime \prime }+\left (1+x \right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\] |
✗ |
✗ |
|
|
\[
{}\left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y = 0
\] |
✓ |
✓ |
|