|
# |
ODE |
Mathematica |
Maple |
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )-z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+10 y \left (t \right )+4 z \left (t \right ), z^{\prime }\left (t \right ) = 5 y \left (t \right )+2 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = 3 y \left (t \right )-z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ), z^{\prime }\left (t \right ) = \frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ), z^{\prime }\left (t \right ) = \frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )-2 z \left (t \right ), z^{\prime }\left (t \right ) = 6 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {x \left (t \right )}{2}, y^{\prime }\left (t \right ) = x \left (t \right )-\frac {y \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {9 x \left (t \right )}{10}+\frac {21 y \left (t \right )}{10}+\frac {16 z \left (t \right )}{5}, y^{\prime }\left (t \right ) = \frac {7 x \left (t \right )}{10}+\frac {13 y \left (t \right )}{2}+\frac {21 z \left (t \right )}{5}, z^{\prime }\left (t \right ) = \frac {11 x \left (t \right )}{10}+\frac {17 y \left (t \right )}{10}+\frac {17 z \left (t \right )}{5}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5}, x_{2}^{\prime }\left (t \right ) = \frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -6 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+5 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 12 x \left (t \right )-9 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )+5 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = 4 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+6 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+6 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-8 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = z \left (t \right ), y^{\prime }\left (t \right ) = -z \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+6 z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-3 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-12 y \left (t \right )-14 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-3 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-2 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )-7, y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+5]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+9 y \left (t \right )+2, y^{\prime }\left (t \right ) = -x \left (t \right )+11 y \left (t \right )+6]
\] |
✓ |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y^{\prime }-y^{2}-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x^{2} y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
✓ |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2}
\] |
✓ |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right )
\] |
✓ |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x^{2}+x +y\right ) {y^{\prime }}^{2}+\left (x^{2}+x y+y\right ) y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
✓ |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y = x y^{\prime }+k {y^{\prime }}^{2}
\] |
✓ |
✓ |
|
|
\[
{}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0
\] |
✓ |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } \left (x y^{\prime }-y+k \right )+a = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\] |
✗ |
✓ |
|
|
\[
{}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
✗ |
✓ |
|
|
\[
{}2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
✗ |
✓ |
|
|
\[
{}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-x y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\] |
✓ |
✓ |
|
|
\[
{}5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y = x y^{\prime }+x^{3} {y^{\prime }}^{2}
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{3}
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\] |
✓ |
✓ |
|
|
\[
{}2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+x^{5}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\beta ^{2} y = 0
\] |
✓ |
✓ |
|