| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=6 \,{\mathrm e}^{2 x -y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.894 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=6 \,{\mathrm e}^{2 x -y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
674.479 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-1+{\mathrm e}^{y} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
135.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-1+{\mathrm e}^{-y} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
133.242 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
195.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3+t +y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
70.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3+t +y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
96.905 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
145.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-x \,{\mathrm e}^{y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
502.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.501 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -2 y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
96.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
86.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y} \sin \left (x \right ) \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
95.716 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
125.106 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{-2 y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
84.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
219.378 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y}+x \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
57.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
57.004 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
84.254 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y}\\ y \left (1\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
251.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 x -2 y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.607 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{y}\\ y \left (0\right )&=-2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
728.295 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{y}\\ y \left (1\right )&={\frac {5}{2}}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
693.509 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 x +2 y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
138.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
81.665 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
104.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
163.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{{\mathrm e}^{x}+1} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
112.218 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
189.057 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
43.245 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=10+{\mathrm e}^{x +y} \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
44.089 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
38.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
73.699 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
86.013 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{-x} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
76.777 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{-2 x}\\ x \left (0\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
80.996 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=t^{2} {\mathrm e}^{-x}\\ x \left (0\right )&=\ln \left (2\right )\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
277.877 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{t +x}\\ x \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
87.128 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
246.899 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
341.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{-x^{2}+y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1496.005 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \,{\mathrm e}^{y}+y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1837.459 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{-y} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
381.659 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{2 x -3 y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
364.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{-y} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
212.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{-y}+1 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
211.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{4 x +3 y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
547.013 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{4 x +3 y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
555.016 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{2 y+10 t} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
326.584 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 y+2 t} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
204.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{t -y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
186.207 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
140.962 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{2 x -y}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
78.604 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
289.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-1&={\mathrm e}^{x +2 y} \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2} {\mathrm e}^{-3 y}\\ y \left (2\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 x -2 y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
149.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
83.783 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=b \,{\mathrm e}^{x}\\ x \left (0\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.916 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y^{\prime }&=x \,{\mathrm e}^{\left (n -1\right ) y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.195 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
266.608 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{x}-t \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.339 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y}\\ y \left (1\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
42.447 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +3 y}+1 \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
135.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1078.774 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
97.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+6 x \,{\mathrm e}^{x -y} \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
129.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-{\mathrm e}^{y}-1 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
116.726 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-{\mathrm e}^{y} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
166.316 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y+t} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
229.632 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{y}\\ y \left (0\right )&=-2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1323.869 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{y}\\ y \left (1\right )&={\frac {5}{2}}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1262.563 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 x +2 y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
428.239 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{3 y} \sin \left (x \right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
263.860 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
271.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-1&={\mathrm e}^{x +2 y} \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
151.922 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&={\mathrm e}^{y}+2 y^{\prime } \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.301 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{-y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }+{\mathrm e}^{t +z}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.691 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x^{2} {\mathrm e}^{y}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.165 |
|