|
# |
ODE |
Mathematica |
Maple |
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 p y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
✓ |
✗ |
|
|
\[
{}\left (1+3 x \right ) x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}3 \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x y = x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+y = x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{3}-x
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime \prime }+x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) x^{2} y^{\prime \prime }-x y^{\prime }+\left (x +2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }-4 y^{\prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (x -1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+p \left (p +1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = t
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y = t^{2}
\] |
✓ |
✓ |
|
|
\[
{}L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}L i^{\prime }+R i = E_{0} \delta \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-5 y = 1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{-t +\pi }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+3 y = 2
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 y = t
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t}
\] |
✓ |
✓ |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\] |
✓ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+t -1, y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )-5 t -2]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-5 t +2, y^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )-8 t -8]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\sqrt {2}\, y \left (t \right ), y^{\prime }\left (t \right ) = \sqrt {2}\, x \left (t \right )-2 y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
✓ |
|