| # | ID | ODE | CAS classification |
Maple |
Mma |
Sympy |
time(sec) |
| \(1\) |
\begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 4 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.056 |
|
| \(2\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t} \\
x_{2}^{\prime }&=x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(3\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t}+t x_{2} \\
x_{2}^{\prime }&=-\frac {x_{1}}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.076 |
|
| \(4\) |
\begin{align*}
x_{1}^{\prime }&=\left (2 t -1\right ) x_{1} \\
x_{2}^{\prime }&={\mathrm e}^{-t^{2}+t} x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.072 |
|
| \(5\) |
\begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0 \\
x^{\prime }+x-y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.046 |
|
| \(6\) |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(7\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.045 |
|
| \(8\) |
\begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t} \\
x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(9\) |
\begin{align*}
x^{\prime \prime }+2 x-2 y^{\prime }&=0 \\
3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(10\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(11\) |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
11.228 |
|
| \(12\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
34.794 |
|
| \(13\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
37.089 |
|
| \(14\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
37.614 |
|
| \(15\) |
\begin{align*}
\left (m +1\right ) x^{m} a \left (m \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
32.151 |
|
| \(16\) |
\begin{align*}
-y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
35.107 |
|
| \(17\) |
\begin{align*}
x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\
y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.061 |
|
| \(18\) |
\begin{align*}
y^{\prime } \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
38.916 |
|
| \(19\) |
\begin{align*}
y^{\prime } \cos \left (y\right )+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
66.856 |
|
| \(20\) |
\begin{align*}
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{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
54.082 |
|
| \(21\) |
\begin{align*}
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{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
76.688 |
|
| \(22\) |
\begin{align*}
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{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
2.456 |
|
| \(23\) |
\begin{align*}
y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
52.832 |
|
| \(24\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
18.919 |
|
| \(25\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
19.987 |
|
| \(26\) |
\begin{align*}
y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
66.183 |
|
| \(27\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
21.480 |
|
| \(28\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
57.424 |
|
| \(29\) |
\begin{align*}
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{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
25.875 |
|
| \(30\) |
\begin{align*}
y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+\ln \left (x \right ) x^{2}}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
25.005 |
|
| \(31\) |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2}-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y+2 x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
101.083 |
|
| \(32\) |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}}-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y+2 x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
100.014 |
|
| \(33\) |
\begin{align*}
-y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
54.825 |
|
| \(34\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
2.639 |
|
| \(35\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(36\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.045 |
|
| \(37\) |
\begin{align*}
x^{\prime }&=x \cos \left (t \right ) \\
y^{\prime }&=x \,{\mathrm e}^{-\sin \left (t \right )} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(38\) |
\begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.026 |
|
| \(39\) |
\begin{align*}
t x^{\prime }+2 x&=t \\
y^{\prime } t -\left (t +2\right ) x-t y&=-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(40\) |
\begin{align*}
t x^{\prime }+2 x-2 y&=t \\
y^{\prime } t +x+5 y&=t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(41\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(42\) |
\begin{align*}
2 x^{\prime }+y^{\prime }-3 x&=0 \\
x^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(43\) |
\begin{align*}
x^{\prime }+x-y^{\prime }&=2 t \\
x^{\prime \prime }+y^{\prime }-9 x+3 y&=\sin \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(44\) |
\begin{align*}
x^{\prime \prime }+a y&=0 \\
y^{\prime \prime }-a^{2} y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.025 |
|
| \(45\) |
\begin{align*}
x^{\prime \prime }&=a x+b y \\
y^{\prime \prime }&=c x+d y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(46\) |
\begin{align*}
x^{\prime \prime }+x+y&=-5 \\
y^{\prime \prime }-4 x-3 y&=-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(47\) |
\begin{align*}
x^{\prime \prime }+6 x+7 y&=0 \\
y^{\prime \prime }+3 x+2 y&=2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(48\) |
\begin{align*}
x^{\prime \prime }-a y^{\prime }+b x&=0 \\
y^{\prime \prime }+a x^{\prime }+b y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(49\) |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }-y^{\prime }+y&=0 \\
y^{\prime \prime \prime }-y^{\prime \prime }+2 x^{\prime }-x&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(50\) |
\begin{align*}
x^{\prime \prime }+y^{\prime \prime }+y^{\prime }&=\sinh \left (2 t \right ) \\
2 x^{\prime \prime }+y^{\prime \prime }&=2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(51\) |
\begin{align*}
x^{\prime \prime }-x^{\prime }+y^{\prime }&=0 \\
x^{\prime \prime }+y^{\prime \prime }-x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.030 |
|
| \(52\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.056 |
|
| \(53\) |
\begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-t x+y \\
\left (t^{2}+1\right ) y^{\prime }&=-x-t y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.047 |
|
| \(54\) |
\begin{align*}
{x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x&=0 \\
x^{\prime } y^{\prime }+y^{\prime } t -y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.074 |
|
| \(55\) |
\begin{align*}
x&=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right ) \\
y&=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.075 |
|
| \(56\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
4.703 |
|
| \(57\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(58\) |
\begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (-1\right ) &= 3 \\
y_{2} \left (-1\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.047 |
|
| \(59\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(60\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(61\) |
\begin{align*}
t x^{\prime }+2 x&=15 y \\
y^{\prime } t&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(62\) |
\begin{align*}
y^{\prime }&=y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
8.025 |
|
| \(63\) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
24.101 |
|
| \(64\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(65\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.080 |
|
| \(66\) |
\begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\
y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(67\) |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(68\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }+x&=0 \\
x^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(69\) |
\begin{align*}
x^{\prime \prime }&=3 x+y \\
y^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(70\) |
\begin{align*}
x^{\prime }&=-\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(71\) |
\begin{align*}
x^{\prime }&=\frac {x}{y} \\
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(72\) |
\begin{align*}
x^{\prime }&=\frac {y}{x-y} \\
y^{\prime }&=\frac {x}{x-y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(73\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(74\) |
\begin{align*}
x^{\prime }&=-2 t x+y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(75\) |
\begin{align*}
x^{\prime }&=-x+t y \\
y^{\prime }&=t x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(76\) |
\begin{align*}
x^{\prime }&=3 x-x^{2} \\
y^{\prime }&=2 x y-3 y+2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(77\) |
\begin{align*}
y^{\prime }&=\frac {z^{2}}{y} \\
z^{\prime }&=\frac {y^{2}}{z} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(78\) |
\begin{align*}
y^{\prime \prime }+z^{\prime }-2 z&={\mathrm e}^{2 x} \\
z^{\prime }+2 y^{\prime }-3 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(79\) |
\begin{align*}
t x^{\prime }-x-3 y&=t \\
y^{\prime } t -x+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(80\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.052 |
|
| \(81\) |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.052 |
|
| \(82\) |
\begin{align*}
y^{\prime }-\frac {\tan \left (y\right )}{x +1}&=\left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
33.743 |
|
| \(83\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
9.343 |
|
| \(84\) |
\begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(85\) |
\begin{align*}
t x^{\prime }&=t -2 x \\
y^{\prime } t&=t x+t y+2 x-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(86\) |
\begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(87\) |
\begin{align*}
x^{\prime \prime \prime }-x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
1.766 |
|
| \(88\) |
\begin{align*}
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{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
0.886 |
|
| \(89\) |
\begin{align*}
x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
0.443 |
|
| \(90\) |
\begin{align*}
x^{\prime }+t y&=-1 \\
x^{\prime }+y^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(91\) |
\begin{align*}
x^{\prime }+y&=3 t \\
y^{\prime }-t x^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(92\) |
\begin{align*}
x^{\prime }&=-x^{3} \\
y^{\prime }&=-y^{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(93\) |
\begin{align*}
y^{\prime \prime }-2 s y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
17.576 |
|
| \(94\) |
\begin{align*}
y^{\prime }&=-\sqrt {1-y^{2}} \\
x^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(95\) |
\begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&=2 y^{2}-x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(96\) |
\begin{align*}
x^{\prime \prime }-x+y&={\mathrm e}^{t} \\
x^{\prime }+x-y^{\prime }-y&=3 \,{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.063 |
|
| \(97\) |
\begin{align*}
y^{\prime }+y-x^{\prime \prime }+x&={\mathrm e}^{t} \\
y^{\prime }-x^{\prime }+x&={\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(98\) |
\begin{align*}
y^{\prime \prime }+z+y&=0 \\
y^{\prime }+z^{\prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(99\) |
\begin{align*}
z^{\prime \prime }+y^{\prime }&=\cos \left (t \right ) \\
y^{\prime \prime }-z&=\sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(100\) |
\begin{align*}
u^{\prime \prime }-2 v&=2 \\
u+v^{\prime }&=5 \,{\mathrm e}^{2 t}+1 \\
\end{align*} With initial conditions \begin{align*}
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 2 \\
v \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.026 |
|
| \(101\) |
\begin{align*}
w^{\prime \prime }-2 z&=0 \\
w^{\prime }+y^{\prime }-z&=2 t \\
w^{\prime }-2 y+z^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
z^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(102\) |
\begin{align*}
y^{\prime }&=\sqrt {y+\sin \left (x \right )}-\cos \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
39.455 |
|
| \(103\) |
\begin{align*}
y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
0.054 |
|
| \(104\) |
\begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime } x -y^{\prime } x -2 y x&=1 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
0.056 |
|
| \(105\) |
\begin{align*}
y^{\prime \prime }&=x \\
y^{\prime \prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(106\) |
\begin{align*}
y^{\prime \prime }&=x-2 \\
y^{\prime \prime }&=2+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(107\) |
\begin{align*}
x^{\prime \prime }+2 y^{\prime }+8 x&=32 t \\
y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= -24 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(108\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right ) \\
y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -1 \\
y \left (0\right ) &= -{\frac {9}{2}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(109\) |
\begin{align*}
x^{\prime \prime }&=-2 y \\
y^{\prime }&=y-x^{\prime } \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 10 \\
y \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(110\) |
\begin{align*}
y^{\prime \prime }&=x-2 \\
x^{\prime \prime }&=2+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(111\) |
\begin{align*}
x^{\prime }+y^{\prime }&=\cos \left (t \right ) \\
x+y^{\prime \prime }&=2 \\
\end{align*} With initial conditions \begin{align*}
x \left (\pi \right ) &= 2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(112\) |
\begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(113\) |
\begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(114\) |
\begin{align*}
x^{\prime \prime }+y^{\prime \prime }&=t \\
x^{\prime \prime }-y^{\prime \prime }&=3 t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(115\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }+6 x&=0 \\
y^{\prime \prime }-x^{\prime }+6 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.058 |
|
| \(116\) |
\begin{align*}
x_{1}^{\prime }&=x_{1}+\left (1-t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.047 |
|
| \(117\) |
\begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(118\) |
\begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (1\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.051 |
|
| \(119\) |
\begin{align*}
x^{\prime }&=-x+x^{2} \\
y^{\prime }&=-3 y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(120\) |
\begin{align*}
y^{\prime }&=-2 \\
z^{\prime }&=x \,{\mathrm e}^{2 x +y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(121\) |
\begin{align*}
y^{\prime } x&=y \\
z^{\prime }&=3 y-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(122\) |
\begin{align*}
y \left (x \tan \left (x \right )+\ln \left (y\right )\right )+\tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
57.309 |
|
| \(123\) |
\begin{align*}
y^{\prime }&=\tan \left (y\right ) \cot \left (x \right )-\sec \left (y\right ) \cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
22.465 |
|
| \(124\) |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y \left (2\right ) &= 0 \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
0.674 |
|
| \(125\) |
\begin{align*}
y^{\prime \prime \prime }+5 y^{\prime \prime }+3 y^{\prime }-9 y&=0 \\
y \left (0\right ) &= -1 \\
y \left (1\right ) &= 0 \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
0.567 |
|
| \(126\) |
\begin{align*}
y_{1}^{\prime }-2 y_{1}&=2 y_{2} \\
y_{2}^{\prime \prime }+2 y_{2}^{\prime }+y_{2}&=-2 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 3 \\
y_{2} \left (0\right ) &= 0 \\
y_{2}^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.025 |
|
| \(127\) |
\begin{align*}
y_{1}^{\prime }+4 y_{1}&=10 y_{2} \\
y_{2}^{\prime \prime }-6 y_{2}^{\prime }+23 y_{2}&=9 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 2 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(128\) |
\begin{align*}
y_{1}^{\prime }-2 y_{1}&=-2 y_{2} \\
y_{2}^{\prime \prime }+y_{2}^{\prime }+6 y_{2}&=4 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 5 \\
y_{2}^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(129\) |
\begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{1}^{\prime }\left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 6 \\
y_{2}^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(130\) |
\begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -1 \\
y_{1}^{\prime }\left (0\right ) &= -4 \\
y_{2} \left (0\right ) &= 1 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(131\) |
\begin{align*}
y_{1}^{\prime }-2 y_{1}&=-y_{2} \\
y_{2}^{\prime \prime }-y_{2}^{\prime }+y_{2}&=y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= -1 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(132\) |
\begin{align*}
y_{1}^{\prime }+2 y_{1}&=5 y_{2} \\
y_{2}^{\prime \prime }-2 y_{2}^{\prime }+5 y_{2}&=2 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
y_{2}^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(133\) |
\begin{align*}
y_{1}^{\prime }&=\sin \left (t \right ) y_{1} \\
y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(134\) |
\begin{align*}
y_{1}^{\prime }&=y_{2} t \\
y_{2}^{\prime }&=-y_{1} t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(135\) |
\begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.057 |
|
| \(136\) |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2} \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (\pi \right ) &= 1 \\
y_{2} \left (\pi \right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.055 |
|
| \(137\) |
\begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.057 |
|
| \(138\) |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -3 \\
y_{2} \left (1\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.054 |
|
| \(139\) |
\begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.058 |
|
| \(140\) |
\begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.067 |
|
| \(141\) |
\begin{align*}
x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\
y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(142\) |
\begin{align*}
y^{\prime \prime }-y+5 y^{\prime }&=t \\
2 y^{\prime }-x^{\prime \prime }+4 x&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(143\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }&=2 \\
x^{\prime \prime }-y^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(144\) |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.016 |
|
| \(145\) |
\begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|