|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+5 \,{\mathrm e}^{x}, y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 \,{\mathrm e}^{-x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )-2 y_{1} \left (x \right )+\sin \left (2 x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+y_{2} \left (x \right )-2 \cos \left (3 x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{3} \left (x \right )-y_{1} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right ) x -x^{2} y_{2} \left (x \right )+4 x, y_{2}^{\prime }\left (x \right ) = {\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right )]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+4 x -2, y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )+3 x]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 5 y_{1} \left (x \right )-5 y_{2} \left (x \right )-5 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+4 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-5 y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 4 y_{1} \left (x \right )+6 y_{2} \left (x \right )+6 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+3 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = -y_{1} \left (x \right )-4 y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+2 y_{2} \left (x \right )-3 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{3} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = -2 y_{1} \left (x \right )-y_{2} \left (x \right )+y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )-2 y_{2} \left (x \right )-y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{2} \left (x \right )-2 y_{3} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+2 y_{2} \left (x \right )+4 y_{3} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+2 y_{2} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{3} \left (x \right )-4 y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 4 y_{3} \left (x \right )+3 y_{4} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-5 y_{3} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-2 y_{1} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{3} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{4} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )+y_{4} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = y_{3} \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -5 x \left (t \right )-y \left (t \right )+2, y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )-3]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )-6, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+2]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {y+1}{t +1}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t^{2} y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t^{4} y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 y+1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2-y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = {\mathrm e}^{-y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime } = 1+x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 t y^{2}+3 y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {t}{y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {t}{y+t^{2} y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t y^{{1}/{3}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {1}{2 y+1}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {2 y+1}{t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y \left (1-y\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {4 t}{1+3 y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} v^{\prime } = t^{2} v-2-2 v+t^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {1}{t y+t +y+1}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y^{2}-4
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} w^{\prime } = \frac {w}{t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \sec \left (y\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime } = -t x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = -y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t^{2} y^{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = -y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {t}{y-t^{2} y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 y+1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t y^{2}+2 y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime } = \frac {t^{2}}{x+t^{3} x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {1-y^{2}}{y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \left (1+y^{2}\right ) t
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {1}{2 y+3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {y^{2}+5}{y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t^{2}+t
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t^{2}+1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 1-2 y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 4 y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 y \left (1-y\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t +y+1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 3 y \left (1-y\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 y-t
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \left (y+\frac {1}{2}\right ) \left (t +y\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \left (t +1\right ) y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
|
✗ |
✓ |
✓ |
|
|
\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
|
✗ |
✓ |
✓ |
|
|
\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
|
✗ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y^{2}+y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y^{2}-y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y^{3}+y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = -t^{2}+2
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t y+t y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t^{2}+t^{2} y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t +t y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t^{2}-2
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \theta ^{\prime } = 2
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} v^{\prime } = -\frac {v}{R C}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} v^{\prime } = \frac {K -v}{R C}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} v^{\prime } = 2 V \left (t \right )-2 v
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 y+1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t -y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = y^{2}-4 t
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \sin \left (y\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} w^{\prime } = \left (3-w\right ) \left (w+1\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} w^{\prime } = \left (3-w\right ) \left (w+1\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\]
|
✗ |
✓ |
✓ |
|