| # | ID | ODE | CAS classification |
Maple |
Mma |
Sympy |
time(sec) |
| \(1\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2}\\ x_{2}^{\prime }&=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.024 |
|
| \(2\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}}{t}\\ x_{2}^{\prime }&=x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.020 |
|
| \(3\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}}{t}+t x_{2}\\ x_{2}^{\prime }&=-\frac {x_{1}}{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.019 |
|
| \(4\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\left (2 t -1\right ) x_{1}\\ x_{2}^{\prime }&={\mathrm e}^{-t^{2}+t} x_{1}+x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.020 |
|
| \(5\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0\\ x^{\prime }+x-y^{\prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.021 |
|
| \(6\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-3 x-4 y&=0\\ x+y^{\prime \prime }+y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.018 |
|
| \(7\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 x+2 y&=\frac {2}{{\mathrm e}^{t}-1}\\ 6 x-y^{\prime }+3 y&=\frac {3}{{\mathrm e}^{t}-1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.020 |
|
| \(8\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t}\\ x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(9\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x-2 y^{\prime }&=0\\ 3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(10\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1}\\ x_{2}^{\prime }&=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(11\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
112.475 |
|
| \(12\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (m +1\right ) x^{m} a \left (m \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
27.138 |
|
| \(13\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
8.872 |
|
| \(14\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=4 y+{\mathrm e}^{t}\\ y^{\prime \prime }&=4 x-{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(15\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right )&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
37.228 |
|
| \(16\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \cos \left (y\right )+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
201.335 |
|
| \(17\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right )&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
75.212 |
|
| \(18\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\left (1+y\right ) \left (\left (y-\ln \left (1+y\right )-\ln \left (x \right )\right ) x +1\right )}{y x} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
53.670 |
|
| \(19\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
1.976 |
|
| \(20\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1} \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
24.809 |
|
| \(21\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1} \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
9.601 |
|
| \(22\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )} \end {array} \]
|
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
10.820 |
|
| \(23\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
35.125 |
|
| \(24\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
10.426 |
|
| \(25\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (x +1\right )} \end {array} \]
|
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
34.021 |
|
| \(26\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{3} \cos \left (2 y\right ) \ln \left (x \right )+x^{3} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
66.880 |
|
| \(27\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+x^{2} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
68.743 |
|
| \(28\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
16.965 |
|
| \(29\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y&=0 \end {array} \]
|
[_Gegenbauer] |
✓ |
✓ |
✓ |
5.857 |
|
| \(30\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x f \left (t \right )+y g \left (t \right )\\ y^{\prime }&=-x g \left (t \right )+y f \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.024 |
|
| \(31\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+\left (a x+b y\right ) f \left (t \right )&=g \left (t \right )\\ y^{\prime }+\left (c x+d y\right ) f \left (t \right )&=h \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.026 |
|
| \(32\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \cos \left (t \right )\\ y^{\prime }&=x \,{\mathrm e}^{-\sin \left (t \right )}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(33\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+y&=0\\ y^{\prime } t +x&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.018 |
|
| \(34\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+2 x&=t\\ y^{\prime } t -\left (t +2\right ) x-t y&=-t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.024 |
|
| \(35\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+2 x-2 y&=t\\ y^{\prime } t +x+5 y&=t^{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(36\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }&=t \left (1-2 \sin \left (t \right )\right ) x+t^{2} y\\ t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }&=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x+t \left (1-t \cos \left (t \right )\right ) y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(37\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }-3 x&=0\\ x^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(38\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-y^{\prime }&=2 t\\ x^{\prime \prime }+y^{\prime }-9 x+3 y&=\sin \left (2 t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.045 |
|
| \(39\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+a y&=0\\ y^{\prime \prime }-a^{2} y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(40\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=a x+b y\\ y^{\prime \prime }&=c x+d y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(41\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x+y&=-5\\ y^{\prime \prime }-4 x-3 y&=-3\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(42\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x+7 y&=0\\ y^{\prime \prime }+3 x+2 y&=2 t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(43\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-a y^{\prime }+b x&=0\\ y^{\prime \prime }+a x^{\prime }+b y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(44\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }-y^{\prime }+y&=0\\ y^{\prime \prime \prime }-y^{\prime \prime }+2 x^{\prime }-x&=t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(45\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime \prime }+y^{\prime }&=\sinh \left (2 t \right )\\ 2 x^{\prime \prime }+y^{\prime \prime }&=2 t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.062 |
|
| \(46\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }+y^{\prime }&=0\\ x^{\prime \prime }+y^{\prime \prime }-x&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.046 |
|
| \(47\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a t x^{\prime }&=b c \left (y-z\right )\\ b t y^{\prime }&=c a \left (z-x\right )\\ c t z^{\prime }&=a b \left (x-y\right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(48\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) x^{\prime }&=-t x+y\\ \left (t^{2}+1\right ) y^{\prime }&=-x-t y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.025 |
|
| \(49\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x&=0\\ x^{\prime } y^{\prime }+y^{\prime } t -y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.063 |
|
| \(50\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x&=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right )\\ y&=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.067 |
|
| \(51\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \end {array} \]
|
[_Gegenbauer] |
✓ |
✓ |
✓ |
9.141 |
|
| \(52\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=\frac {y^{2}}{x}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(53\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(54\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(55\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(56\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+2 x&=15 y\\ y^{\prime } t&=x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.053 |
|
| \(57\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
14.955 |
|
| \(58\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=\frac {y^{2}}{x}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(59\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}}\\ x_{2}^{\prime }&=x_{2}-x_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(60\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {{\mathrm e}^{-x}}{t}\\ y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(61\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y\\ y^{\prime \prime }&=x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(62\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime }+x&=0\\ x^{\prime }+y^{\prime \prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(63\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=3 x+y\\ y^{\prime }&=-2 x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(64\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {1}{y}\\ y^{\prime }&=\frac {1}{x}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(65\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {x}{y}\\ y^{\prime }&=\frac {y}{x}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(66\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {y}{x-y}\\ y^{\prime }&=\frac {x}{x-y}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(67\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1}\\ y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.030 |
|
| \(68\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 t x+y\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.025 |
|
| \(69\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+t y\\ y^{\prime }&=t x-y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.021 |
|
| \(70\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-x^{2}\\ y^{\prime }&=2 x y-3 y+2\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(71\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {z^{2}}{y}\\ z^{\prime }&=\frac {y^{2}}{z}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(72\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+z^{\prime }-2 z&={\mathrm e}^{2 x}\\ z^{\prime }+2 y^{\prime }-3 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(73\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }-x-3 y&=t\\ y^{\prime } t -x+y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(74\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+6 x-y-3 z&=0\\ y^{\prime } t +23 x-6 y-9 z&=0\\ t z^{\prime }+x+y-2 z&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.049 |
|
| \(75\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-3 x-4 y&=0\\ x+y^{\prime \prime }+y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(76\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {\tan \left (y\right )}{x +1}&=\left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right ) \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
130.940 |
|
| \(77\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
288.439 |
|
| \(78\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+y&=0\\ y^{\prime } t +x&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.021 |
|
| \(79\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=t -2 x\\ y^{\prime } t&=t x+t y+2 x-t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.024 |
|
| \(80\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \cos \left (t \right )-\sin \left (t \right ) y\\ y^{\prime }&=x \sin \left (t \right )+y \cos \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.019 |
|
| \(81\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime }-x^{\prime }&=0\\ x \left (0\right )&=1\\ x \left (\infty \right )&=0\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
2.962 |
|
| \(82\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime \prime }-4 x^{\prime \prime }+x&=0\\ x \left (0\right )&=0\\ x \left (\infty \right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
12.342 |
|
| \(83\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+t y&=-1\\ x^{\prime }+y^{\prime }&=2\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.026 |
|
| \(84\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y&=3 t\\ y^{\prime }-t x^{\prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(85\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x^{3}\\ y^{\prime }&=-y^{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(86\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\sqrt {1-y^{2}}\\ x^{\prime }&=x+2 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(87\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}\\ y^{\prime }&=2 y^{2}-x y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(88\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x+y&={\mathrm e}^{t}\\ x^{\prime }+x-y^{\prime }-y&=3 \,{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.045 |
|
| \(89\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y-x^{\prime \prime }+x&={\mathrm e}^{t}\\ y^{\prime }-x^{\prime }+x&={\mathrm e}^{-t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.046 |
|
| \(90\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+z+y&=0\\ y^{\prime }+z^{\prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.053 |
|
| \(91\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime \prime }+y^{\prime }&=\cos \left (t \right )\\ y^{\prime \prime }-z&=\sin \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.056 |
|
| \(92\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }-2 v&=2\\ u+v^{\prime }&=5 \,{\mathrm e}^{2 t}+1\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.049 |
|
| \(93\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime \prime }-2 z&=0\\ w^{\prime }+y^{\prime }-z&=2 t\\ w^{\prime }-2 y+z^{\prime \prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.075 |
|
| \(94\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y+\sin \left (x \right )}-\cos \left (x \right ) \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
53.288 |
|
| \(95\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
0.151 |
|
| \(96\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }+2 y^{\prime \prime } x -y^{\prime } x -2 y x&=1 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
0.141 |
|
| \(97\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x\\ y^{\prime \prime }&=y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.020 |
|
| \(98\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x-2\\ y^{\prime \prime }&=2+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(99\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 y^{\prime }+8 x&=32 t\\ y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.046 |
|
| \(100\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right )\\ y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(101\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=-2 y\\ y^{\prime }&=y-x^{\prime }\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.034 |
|
| \(102\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x-2\\ x^{\prime \prime }&=2+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(103\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }&=\cos \left (t \right )\\ x+y^{\prime \prime }&=2\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(104\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t}\\ y^{\prime \prime }&=x-{\mathrm e}^{-2 t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(105\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t}\\ y^{\prime \prime }&=x-{\mathrm e}^{-2 t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(106\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime \prime }&=t\\ x^{\prime \prime }-y^{\prime \prime }&=3 t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.066 |
|
| \(107\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime }+6 x&=0\\ y^{\prime \prime }-x^{\prime }+6 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.059 |
|
| \(108\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+\left (1-t \right ) x_{2}\\ x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(109\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=3 x-2 y\\ y^{\prime } t&=x+y-t^{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(110\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=3 x-2 y\\ y^{\prime } t&=x+y-t^{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(111\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+x^{2}\\ y^{\prime }&=-3 y+x y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.045 |
|
| \(112\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-2\\ z^{\prime }&=x \,{\mathrm e}^{2 x +y}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(113\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=y\\ z^{\prime }&=3 y-x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(114\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (x \tan \left (x \right )+\ln \left (y\right )\right )+\tan \left (x \right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
86.959 |
|
| \(115\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\tan \left (y\right ) \cot \left (x \right )-\sec \left (y\right ) \cos \left (x \right ) \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
325.100 |
|
| \(116\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-2 y_{1}&=2 y_{2}\\ y_{2}^{\prime \prime }+2 y_{2}^{\prime }+y_{2}&=-2 y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.046 |
|
| \(117\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }+4 y_{1}&=10 y_{2}\\ y_{2}^{\prime \prime }-6 y_{2}^{\prime }+23 y_{2}&=9 y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(118\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-2 y_{1}&=-2 y_{2}\\ y_{2}^{\prime \prime }+y_{2}^{\prime }+6 y_{2}&=4 y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.046 |
|
| \(119\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime \prime }+2 y_{1}^{\prime }+6 y_{1}&=5 y_{2}\\ y_{2}^{\prime \prime }-2 y_{2}^{\prime }+6 y_{2}&=9 y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.062 |
|
| \(120\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime \prime }+2 y_{1}&=-3 y_{2}\\ y_{2}^{\prime \prime }+2 y_{2}^{\prime }-9 y_{2}&=6 y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(121\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-2 y_{1}&=-y_{2}\\ y_{2}^{\prime \prime }-y_{2}^{\prime }+y_{2}&=y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(122\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }+2 y_{1}&=5 y_{2}\\ y_{2}^{\prime \prime }-2 y_{2}^{\prime }+5 y_{2}&=2 y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.045 |
|
| \(123\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\sin \left (t \right ) y_{1}\\ y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(124\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2} t\\ y_{2}^{\prime }&=-y_{1} t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.030 |
|
| \(125\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1} t +y_{2} t\\ y_{2}^{\prime }&=-y_{1} t -y_{2} t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(126\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2}\\ y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(127\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\left (2 t +1\right ) y_{1}+2 y_{2} t\\ y_{2}^{\prime }&=-2 y_{1} t +\left (1-2 t \right ) y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(128\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}\\ y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(129\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {4 t y_{1}}{t^{2}+1}+\frac {6 y_{2} t}{t^{2}+1}-3 t\\ y_{2}^{\prime }&=-\frac {2 t y_{1}}{t^{2}+1}-\frac {4 y_{2} t}{t^{2}+1}+t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.034 |
|
| \(130\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t\\ y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(131\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=4 y+{\mathrm e}^{t}\\ y^{\prime \prime }&=4 x-{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.030 |
|
| \(132\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y+5 y^{\prime }&=t\\ 2 y^{\prime }-x^{\prime \prime }+4 x&=2\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.058 |
|
| \(133\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime }&=2\\ x^{\prime \prime }-y^{\prime \prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(134\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y\\ y^{\prime \prime }&=x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.016 |
|
| \(135\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {1}{y}\\ y^{\prime }&=\frac {1}{x}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.021 |
|
| \(136\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) \ln \left (x^{2}+1\right ) y^{\prime }-2 y x&=\ln \left (x^{2}+1\right )-2 x \arctan \left (x \right )\\ y \left (-\infty \right )&=-\frac {\pi }{2}\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
152.981 |
|
| \(137\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime }&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0\\ y \left (0\right )&=y_{0}\\ \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
7.773 |
|
| \(138\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \cos \left (t \right )\\ 2 y^{\prime }&=\left ({\mathrm e}^{t}+{\mathrm e}^{-t}\right ) y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(139\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {1}{y}\\ y^{\prime }&=\frac {1}{x}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(140\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=t -2 x\\ y^{\prime } t&=t x+t y+2 x-t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(141\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}+3 \ln \left (y\right )\right ) y&=y^{\prime } x \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
18.997 |
|
| \(142\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\left (3 x +y^{3}-1\right )^{2}}{y^{2}} \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
72.204 |
|
| \(143\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime } x -x^{2} \sqrt {1+y^{2}}&=\left (x +1\right ) \left (1+y^{2}\right ) \end {array} \]
|
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
50.224 |
|
| \(144\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}-1+\left (y^{2} x^{2}+x^{3}+x \right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
70.276 |
|
| \(145\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
9.990 |
|
| \(146\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=2 x-3 y\\ y^{\prime \prime }&=x-2 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(147\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=3 x+4 y\\ y^{\prime \prime }&=-x-y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.024 |
|
| \(148\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=2 y\\ y^{\prime \prime }&=-2 x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(149\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=3 x-y-z\\ y^{\prime \prime }&=-x+3 y-z\\ z^{\prime \prime }&=-x-y+3 z\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.030 |
|
| \(150\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0\\ x^{\prime }+x-y^{\prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.052 |
|
| \(151\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x+2 y^{\prime \prime }-2 y&=0\\ x^{\prime }-x+y^{\prime }+y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.026 |
|
| \(152\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x-2 y^{\prime }&=0\\ 3 x^{\prime }+y^{\prime \prime }-8 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(153\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+5 x^{\prime }+2 y^{\prime }+y&=0\\ 3 x^{\prime \prime }+5 x+y^{\prime }+3 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(154\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }-2 x-2 y^{\prime }-y&=0\\ x^{\prime \prime }-4 x^{\prime }-y^{\prime \prime }+2 y^{\prime }+2 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(155\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime \prime }+2 x^{\prime }+x+3 y^{\prime \prime }+y^{\prime }+y&=0\\ x^{\prime \prime }+4 x^{\prime }-x+3 y^{\prime \prime }+2 y^{\prime }-y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.034 |
|
| \(156\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1}\\ y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.019 |
|
| \(157\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x}{z}\\ z^{\prime }&=-\frac {x}{y}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
0.022 |
|