| # | ID | ODE | CAS classification |
Maple |
Mma |
Sympy |
time(sec) |
| \(1\) |
\begin{align*}
x^{\prime }&=t x-{\mathrm e}^{t} y+\cos \left (t \right ) \\
y^{\prime }&={\mathrm e}^{-t} x+t^{2} y-\sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.052 |
|
| \(2\) |
\begin{align*}
x^{\prime }&=t x-y+{\mathrm e}^{t} z \\
y^{\prime }&=2 x+t^{2} y-z \\
z^{\prime }&={\mathrm e}^{-t} x+3 t y+t^{3} z \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.060 |
|
| \(3\) |
\begin{align*}
x^{\prime }&=x-x^{2}-2 x y \\
y^{\prime }&=2 y-2 y^{2}-3 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.037 |
|
| \(4\) |
\begin{align*}
x^{\prime }&=-b x y+m \\
y^{\prime }&=b x y-g y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.063 |
|
| \(5\) |
\begin{align*}
x^{\prime }&=a x-b x y \\
y^{\prime }&=-c y+d x y \\
z^{\prime }&=z+x^{2}+y^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.049 |
|
| \(6\) |
\begin{align*}
x^{\prime }&=-x-x \,y^{2} \\
y^{\prime }&=-y-y \,x^{2} \\
z^{\prime }&=1-z+x^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.044 |
|
| \(7\) |
\begin{align*}
x^{\prime }&=x \,y^{2}-x \\
y^{\prime }&=x \sin \left (\pi y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.034 |
|
| \(8\) |
\begin{align*}
x^{\prime }&=\cos \left (y\right ) \\
y^{\prime }&=\sin \left (x\right )-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.035 |
|
| \(9\) |
\begin{align*}
x^{\prime }&=-1-y-{\mathrm e}^{x} \\
y^{\prime }&=x^{2}+y \left ({\mathrm e}^{x}-1\right ) \\
z^{\prime }&=x+\sin \left (z\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.047 |
|
| \(10\) |
\begin{align*}
x^{\prime }&=x-y^{2} \\
y^{\prime }&=x^{2}-y \\
z^{\prime }&={\mathrm e}^{z}-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.124 |
|
| \(11\) |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-\frac {\left (x_{1}^{2}+\sqrt {x_{1}^{2}+4 x_{2}^{2}}\right ) x_{1}}{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.037 |
|
| \(12\) |
\begin{align*}
x^{\prime }&=x-x^{3}-x y \\
y^{\prime }&=2 y-y^{5}-y \,x^{4} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.038 |
|
| \(13\) |
\begin{align*}
x^{\prime }&=x^{2}+y^{2}+1 \\
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.033 |
|
| \(14\) |
\begin{align*}
x^{\prime }&=x^{2}+y^{2}-1 \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.037 |
|
| \(15\) |
\begin{align*}
x^{\prime }&=6 x-6 x^{2}-2 x y \\
y^{\prime }&=4 y-4 y^{2}-2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.038 |
|
| \(16\) |
\begin{align*}
x^{\prime }&=\tan \left (x+y\right ) \\
y^{\prime }&=x+x^{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.073 |
|
| \(17\) |
\begin{align*}
x^{\prime }&={\mathrm e}^{y}-x \\
y^{\prime }&={\mathrm e}^{x}+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.063 |
|
| \(18\) |
\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 |
|
| \(19\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t} \\
x_{2}^{\prime }&=x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(20\) |
\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 |
|
| \(21\) |
\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 |
|
| \(22\) |
\begin{align*}
x_{1}^{\prime }&=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2} \\
x_{2}^{\prime }&=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right ) \\
x_{3}^{\prime }&=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-t \cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.064 |
|
| \(23\) |
\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 |
|
| \(24\) |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(25\) |
\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 |
|
| \(26\) |
\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 |
|
| \(27\) |
\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 |
|
| \(28\) |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.044 |
|
| \(29\) |
\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 |
|
| \(30\) |
\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 |
|
| \(31\) |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+x y_{3} \\
y_{2}^{\prime }&=y_{2}+x^{3} y_{3} \\
y_{3}^{\prime }&=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.041 |
|
| \(32\) |
\begin{align*}
x^{\prime }&=x y+1 \\
y^{\prime }&=-x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.035 |
|
| \(33\) |
\begin{align*}
x^{\prime }&=t y+1 \\
y^{\prime }&=-t x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.031 |
|
| \(34\) |
\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 |
|
| \(35\) |
\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 |
|
| \(36\) |
\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 |
|
| \(37\) |
\begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.026 |
|
| \(38\) |
\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 |
|
| \(39\) |
\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 |
|
| \(40\) |
\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 |
|
| \(41\) |
\begin{align*}
x^{\prime }+y^{\prime }+y&=f \left (t \right ) \\
x^{\prime \prime }+y^{\prime \prime }+y^{\prime }+x+y&=g \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.037 |
|
| \(42\) |
\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 }-x+2 y&=0 \\
x^{\prime \prime }-2 y^{\prime }&=2 t -\cos \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(45\) |
\begin{align*}
t x^{\prime }-y^{\prime } t -2 y&=0 \\
t x^{\prime \prime }+2 x^{\prime }+t x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.034 |
|
| \(46\) |
\begin{align*}
x^{\prime \prime }+a y&=0 \\
y^{\prime \prime }-a^{2} y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.025 |
|
| \(47\) |
\begin{align*}
x^{\prime \prime }&=a x+b y \\
y^{\prime \prime }&=c x+d y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(48\) |
\begin{align*}
x^{\prime \prime }&=a_{1} x+b_{1} y+c_{1} \\
y^{\prime \prime }&=a_{2} x+b_{2} y+c_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.025 |
|
| \(49\) |
\begin{align*}
x^{\prime \prime }+x+y&=-5 \\
y^{\prime \prime }-4 x-3 y&=-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(50\) |
\begin{align*}
x^{\prime \prime }&=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x+\frac {3 c^{2} y \sin \left (2 a t b \right )}{2} \\
y^{\prime \prime }&=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y+\frac {3 c^{2} x \sin \left (2 a t b \right )}{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.036 |
|
| \(51\) |
\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 |
|
| \(52\) |
\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 |
|
| \(53\) |
\begin{align*}
a_{1} x^{\prime \prime }+b_{1} x^{\prime }+c_{1} x-A y^{\prime }&=B \,{\mathrm e}^{i \omega t} \\
a_{2} y^{\prime \prime }+b_{2} y^{\prime }+c_{2} y+A x^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.057 |
|
| \(54\) |
\begin{align*}
x^{\prime \prime }+a \left (x^{\prime }-y^{\prime }\right )+b_{1} x&=c_{1} {\mathrm e}^{i \omega t} \\
y^{\prime \prime }+a \left (y^{\prime }-x^{\prime }\right )+b_{2} y&=c_{2} {\mathrm e}^{i \omega t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.048 |
|
| \(55\) |
\begin{align*}
\operatorname {a11} x^{\prime \prime }+\operatorname {b11} x^{\prime }+\operatorname {c11} x+\operatorname {a12} y^{\prime \prime }+\operatorname {b12} y^{\prime }+\operatorname {c12} y&=0 \\
\operatorname {a21} x^{\prime \prime }+\operatorname {b21} x^{\prime }+\operatorname {c21} x+\operatorname {a22} y^{\prime \prime }+\operatorname {b22} y^{\prime }+\operatorname {c22} y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.063 |
|
| \(56\) |
\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 |
|
| \(57\) |
\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 |
|
| \(58\) |
\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 |
|
| \(59\) |
\begin{align*}
x^{\prime }&=a x+g y+\beta z \\
y^{\prime }&=g x+b y+\alpha z \\
z^{\prime }&=\beta x+\alpha y+c z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
86.938 |
|
| \(60\) |
\begin{align*}
t x^{\prime }&=2 x-t \\
t^{3} y^{\prime }&=-x+t^{2} y+t \\
t^{4} z^{\prime }&=-x-t^{2} y+t^{3} z+t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.050 |
|
| \(61\) |
\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 |
|
| \(62\) |
\begin{align*}
x_{1}^{\prime }&=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right ) \\
x_{2}^{\prime }&=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right ) \\
x_{3}^{\prime }&=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4} \\
x_{4}^{\prime }&=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.080 |
|
| \(63\) |
\begin{align*}
x^{\prime }&=-x \left (x+y\right ) \\
y^{\prime }&=y \left (x+y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(64\) |
\begin{align*}
x^{\prime }&=\left (a y+b \right ) x \\
y^{\prime }&=\left (c x+d \right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.033 |
|
| \(65\) |
\begin{align*}
x^{\prime }&=x \left (a \left (p x+q y\right )+\alpha \right ) \\
y^{\prime }&=y \left (\beta +b \left (p x+q y\right )\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.044 |
|
| \(66\) |
\begin{align*}
x^{\prime }&=h \left (a -x\right ) \left (c -x-y\right ) \\
y^{\prime }&=k \left (b -y\right ) \left (c -x-y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.034 |
|
| \(67\) |
\begin{align*}
x^{\prime }&=y^{2}-\cos \left (x\right ) \\
y^{\prime }&=-y \sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(68\) |
\begin{align*}
x^{\prime }&=-x \,y^{2}+x+y \\
y^{\prime }&=y \,x^{2}-x-y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.032 |
|
| \(69\) |
\begin{align*}
x^{\prime }&=x+y-x \left (x^{2}+y^{2}\right ) \\
y^{\prime }&=-x+y-y \left (x^{2}+y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.045 |
|
| \(70\) |
\begin{align*}
x^{\prime }&=-y+x \left (x^{2}+y^{2}-1\right ) \\
y^{\prime }&=x+y \left (x^{2}+y^{2}-1\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.034 |
|
| \(71\) |
\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 |
|
| \(72\) |
\begin{align*}
\left (x^{2}+y^{2}-t^{2}\right ) x^{\prime }&=-2 t x \\
\left (x^{2}+y^{2}-t^{2}\right ) y^{\prime }&=-2 t y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.052 |
|
| \(73\) |
\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 |
|
| \(74\) |
\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 |
|
| \(75\) |
\begin{align*}
x^{\prime \prime }&=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2} \\
y^{\prime \prime }&={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.045 |
|
| \(76\) |
\begin{align*}
x^{\prime \prime }&=\frac {k x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\
y^{\prime \prime }&=\frac {k y}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.028 |
|
| \(77\) |
\begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x^{2}+y \\
z^{\prime }&=x^{2}+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.049 |
|
| \(78\) |
\begin{align*}
a x^{\prime }&=\left (b -c \right ) y z \\
b y^{\prime }&=\left (c -a \right ) z x \\
c z^{\prime }&=\left (a -b \right ) x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.048 |
|
| \(79\) |
\begin{align*}
x^{\prime }&=x \left (y-z\right ) \\
y^{\prime }&=y \left (z-x\right ) \\
z^{\prime }&=z \left (x-y\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.060 |
|
| \(80\) |
\begin{align*}
x^{\prime }+y^{\prime }&=x y \\
y^{\prime }+z^{\prime }&=y z \\
x^{\prime }+z^{\prime }&=x z \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.051 |
|
| \(81\) |
\begin{align*}
x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24} \\
y^{\prime }&=2 x y-3 z \\
z^{\prime }&=3 x z-\frac {y^{2}}{6} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.050 |
|
| \(82\) |
\begin{align*}
x^{\prime }&=x \left (y^{2}-z^{2}\right ) \\
y^{\prime }&=y \left (z^{2}-x^{2}\right ) \\
z^{\prime }&=z \left (x^{2}-y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.040 |
|
| \(83\) |
\begin{align*}
x^{\prime }&=x \left (y^{2}-z^{2}\right ) \\
y^{\prime }&=-y \left (z^{2}+x^{2}\right ) \\
z^{\prime }&=z \left (x^{2}+y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.051 |
|
| \(84\) |
\begin{align*}
x^{\prime }&=-x \,y^{2}+x+y \\
y^{\prime }&=y \,x^{2}-x-y \\
z^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.039 |
|
| \(85\) |
\begin{align*}
\left (x-y\right ) \left (x-z\right ) x^{\prime }&=f \left (t \right ) \\
\left (-x+y\right ) \left (y-z\right ) y^{\prime }&=f \left (t \right ) \\
\left (z-x\right ) \left (z-y\right ) z^{\prime }&=f \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.060 |
|
| \(86\) |
\begin{align*}
x^{\prime }&=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\
y^{\prime }&=4 x+4 y-y \left (x^{2}+y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.038 |
|
| \(87\) |
\begin{align*}
x^{\prime }&=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\
y^{\prime }&=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.053 |
|
| \(88\) |
\begin{align*}
x^{\prime }&=x-x^{2} \\
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.026 |
|
| \(89\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(90\) |
\begin{align*}
y_{1}^{\prime }&=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\
y_{2}^{\prime }&=2 y_{1}+1-6 x \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -2 \\
y_{2} \left (1\right ) &= -5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.040 |
|
| \(91\) |
\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 |
|
| \(92\) |
\begin{align*}
y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\
y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.047 |
|
| \(93\) |
\begin{align*}
y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\
y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (2\right ) &= 1 \\
y_{2} \left (2\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.049 |
|
| \(94\) |
\begin{align*}
y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.045 |
|
| \(95\) |
\begin{align*}
y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (3\right ) &= 1 \\
y_{2} \left (3\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.045 |
|
| \(96\) |
\begin{align*}
y_{1}^{\prime }&=2 x y_{1}-x^{2} y_{2}+4 x \\
y_{2}^{\prime }&={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.042 |
|
| \(97\) |
\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 |
|
| \(98\) |
\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 |
|
| \(99\) |
\begin{align*}
t x^{\prime }+2 x&=15 y \\
y^{\prime } t&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(100\) |
\begin{align*}
x^{\prime }&=x y-6 y \\
y^{\prime }&=x-y-5 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.037 |
|
| \(101\) |
\begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.025 |
|
| \(102\) |
\begin{align*}
x_{1}^{\prime }&=-2 t x_{1}^{2} \\
x_{2}^{\prime }&=\frac {x_{2}+t}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(103\) |
\begin{align*}
x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\
x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.087 |
|
| \(104\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(105\) |
\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 |
|
| \(106\) |
\begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\
y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(107\) |
\begin{align*}
x^{\prime }&=\frac {y+t}{x+y} \\
y^{\prime }&=\frac {x-t}{x+y} \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.044 |
|
| \(108\) |
\begin{align*}
x^{\prime }&=\frac {t -y}{-x+y} \\
y^{\prime }&=\frac {x-t}{-x+y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.045 |
|
| \(109\) |
\begin{align*}
x^{\prime }&=\frac {y+t}{x+y} \\
y^{\prime }&=\frac {t +x}{x+y} \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.067 |
|
| \(110\) |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(111\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }+x&=0 \\
x^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(112\) |
\begin{align*}
x^{\prime \prime }&=3 x+y \\
y^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(113\) |
\begin{align*}
x^{\prime \prime }&=x^{2}+y \\
y^{\prime }&=-2 x x^{\prime }+x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.026 |
|
| \(114\) |
\begin{align*}
x^{\prime }&=x^{2}+y^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.088 |
|
| \(115\) |
\begin{align*}
x^{\prime }&=-\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(116\) |
\begin{align*}
x^{\prime }&=\frac {x}{y} \\
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(117\) |
\begin{align*}
x^{\prime }&=\frac {y}{x-y} \\
y^{\prime }&=\frac {x}{x-y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(118\) |
\begin{align*}
x^{\prime }&=\sin \left (x\right ) \cos \left (y\right ) \\
y^{\prime }&=\cos \left (x\right ) \sin \left (y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.046 |
|
| \(119\) |
\begin{align*}
{\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\
{\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.058 |
|
| \(120\) |
\begin{align*}
x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\
y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.053 |
|
| \(121\) |
\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 |
|
| \(122\) |
\begin{align*}
x^{\prime }&=-2 t x+y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(123\) |
\begin{align*}
x^{\prime }&=-x+t y \\
y^{\prime }&=t x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(124\) |
\begin{align*}
x^{\prime }&=x+y+4 \\
y^{\prime }&=-2 x+\sin \left (t \right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.041 |
|
| \(125\) |
\begin{align*}
x^{\prime }&=-x+y+x^{2} \\
y^{\prime }&=y-2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.037 |
|
| \(126\) |
\begin{align*}
x^{\prime }&=2 y \,x^{2}-3 x^{2}-4 y \\
y^{\prime }&=-2 x \,y^{2}+6 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(127\) |
\begin{align*}
x^{\prime }&=3 x-x^{2} \\
y^{\prime }&=2 x y-3 y+2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(128\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=y+2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.044 |
|
| \(129\) |
\begin{align*}
x^{\prime }&=2-y \\
y^{\prime }&=y-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.041 |
|
| \(130\) |
\begin{align*}
x^{\prime }&=x-x^{2}-x y \\
y^{\prime }&=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.044 |
|
| \(131\) |
\begin{align*}
x^{\prime }&=-\left (x-y\right ) \left (1-x-y\right ) \\
y^{\prime }&=x \left (2+y\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.037 |
|
| \(132\) |
\begin{align*}
x^{\prime }&=y \left (2-x-y\right ) \\
y^{\prime }&=-x-y-2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.050 |
|
| \(133\) |
\begin{align*}
x^{\prime }&=\left (2+x\right ) \left (-x+y\right ) \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.040 |
|
| \(134\) |
\begin{align*}
x^{\prime }&=-x+2 x y \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.037 |
|
| \(135\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x-\frac {x^{3}}{5}-\frac {y}{5} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.036 |
|
| \(136\) |
\begin{align*}
x^{\prime }&=x \left (1-x-y\right ) \\
y^{\prime }&=y \left (\frac {3}{4}-y-\frac {x}{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.061 |
|
| \(137\) |
\begin{align*}
x^{\prime }&=-2 y+x y \\
y^{\prime }&=x+4 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(138\) |
\begin{align*}
x^{\prime }&=1+5 y \\
y^{\prime }&=1-6 x^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.045 |
|
| \(139\) |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {y}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.035 |
|
| \(140\) |
\begin{align*}
y^{\prime }&=1-\frac {1}{z} \\
z^{\prime }&=\frac {1}{-x +y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.045 |
|
| \(141\) |
\begin{align*}
y^{\prime }&=\frac {z^{2}}{y} \\
z^{\prime }&=\frac {y^{2}}{z} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(142\) |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {z^{2}}{y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.040 |
|
| \(143\) |
\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 |
|
| \(144\) |
\begin{align*}
y^{\prime }+\frac {2 z}{x^{2}}&=1 \\
z^{\prime }+y&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(145\) |
\begin{align*}
t x^{\prime }-x-3 y&=t \\
y^{\prime } t -x+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(146\) |
\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 |
|
| \(147\) |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.052 |
|
| \(148\) |
\begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(149\) |
\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 |
|
| \(150\) |
\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 |
|
| \(151\) |
\begin{align*}
x^{\prime }&=\left (3 t -1\right ) x-\left (1-t \right ) y+t \,{\mathrm e}^{t^{2}} \\
y^{\prime }&=-\left (t +2\right ) x+\left (-2+t \right ) y-{\mathrm e}^{t^{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.048 |
|
| \(152\) |
\begin{align*}
w_{1}^{\prime }&=w_{2} \\
w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(153\) |
\begin{align*}
x^{\prime }+t y&=-1 \\
x^{\prime }+y^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(154\) |
\begin{align*}
x^{\prime }+y&=3 t \\
y^{\prime }-t x^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(155\) |
\begin{align*}
x^{\prime }-t y&=1 \\
y^{\prime }-t x^{\prime }&=3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.040 |
|
| \(156\) |
\begin{align*}
t^{2} x^{\prime }-y&=1 \\
y^{\prime }-2 x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(157\) |
\begin{align*}
t x^{\prime }+y^{\prime }&=1 \\
y^{\prime }+x+{\mathrm e}^{x^{\prime }}&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.133 |
|
| \(158\) |
\begin{align*}
x x^{\prime }+y&=2 t \\
y^{\prime }+2 x^{2}&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.039 |
|
| \(159\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.046 |
|
| \(160\) |
\begin{align*}
x^{\prime }&=2 x-7 x y-a x \\
y^{\prime }&=-y+4 x y-a y \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.039 |
|
| \(161\) |
\begin{align*}
x^{\prime }&=2 x-2 x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.048 |
|
| \(162\) |
\begin{align*}
x^{\prime }&=x-4 x y \\
y^{\prime }&=-2 y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(163\) |
\begin{align*}
x^{\prime }&=x \left (3-y\right ) \\
y^{\prime }&=y \left (x-5\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(164\) |
\begin{align*}
x^{\prime }&=-x+y+y^{2} \\
y^{\prime }&=-2 y-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.049 |
|
| \(165\) |
\begin{align*}
x^{\prime }&=-x^{3} \\
y^{\prime }&=-y^{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(166\) |
\begin{align*}
y^{\prime }&=-\sqrt {1-y^{2}} \\
x^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(167\) |
\begin{align*}
x^{\prime }&=x+4 y-y^{2} \\
y^{\prime }&=6 x-y+2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.056 |
|
| \(168\) |
\begin{align*}
x^{\prime }&=\sin \left (x\right )-4 y \\
y^{\prime }&=\sin \left (2 x\right )-5 y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(169\) |
\begin{align*}
x^{\prime }&=8 x-y^{2} \\
y^{\prime }&=6 x^{2}-6 y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.051 |
|
| \(170\) |
\begin{align*}
x^{\prime }&=-x^{2}-y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.049 |
|
| \(171\) |
\begin{align*}
x^{\prime }&=-x^{3}-y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(172\) |
\begin{align*}
x^{\prime }&=2 x y \\
y^{\prime }&=3 y^{2}-x^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.052 |
|
| \(173\) |
\begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&=2 y^{2}-x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(174\) |
\begin{align*}
x^{\prime }&=-x+y^{2} \\
y^{\prime }&=x^{2}-y \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.039 |
|
| \(175\) |
\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 |
|
| \(176\) |
\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 |
|
| \(177\) |
\begin{align*}
x^{\prime \prime }&=1 \\
x^{\prime }+x+y^{\prime \prime }-9 y+z^{\prime }+z&=0 \\
5 x+z^{\prime \prime }-4 z&=2 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.051 |
|
| \(178\) |
\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 |
|
| \(179\) |
\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 |
|
| \(180\) |
\begin{align*}
w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t} \\
-2 w^{\prime }+2 y^{\prime }+z&=0 \\
2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 2 \\
z^{\prime }\left (0\right ) &= -2 \\
w \left (0\right ) &= 1 \\
w^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.056 |
|
| \(181\) |
\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 |
|
| \(182\) |
\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 |
|
| \(183\) |
\begin{align*}
w^{\prime \prime }+y+z&=-1 \\
w+y^{\prime \prime }-z&=0 \\
-w-y^{\prime }+z^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.040 |
|
| \(184\) |
\begin{align*}
y^{\prime \prime }&=x \\
y^{\prime \prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(185\) |
\begin{align*}
y^{\prime \prime }&=x-2 \\
y^{\prime \prime }&=2+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(186\) |
\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 |
|
| \(187\) |
\begin{align*}
x^{\prime }+3 y^{\prime }&=x y \\
3 x^{\prime }-y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.054 |
|
| \(188\) |
\begin{align*}
r^{\prime \prime }\left (t \right )&=r \left (t \right )+y \\
y^{\prime \prime }&=5 r \left (t \right )-3 y+t^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
0.039 |
|
| \(189\) |
\begin{align*}
x y^{\prime }+y x^{\prime }&=t^{2} \\
2 x^{\prime \prime }-y^{\prime }&=5 t \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.049 |
|
| \(190\) |
\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 |
|
| \(191\) |
\begin{align*}
x^{\prime }&=y z \\
y^{\prime }&=x z \\
z^{\prime }&=x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.051 |
|
| \(192\) |
\begin{align*}
x^{\prime }&=x y \\
y^{\prime }&=1+y^{2} \\
z^{\prime }&=z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.049 |
|
| \(193\) |
\begin{align*}
t^{2} y^{\prime \prime }+t z^{\prime }+z&=t \\
y^{\prime } t +z&=\ln \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.047 |
|
| \(194\) |
\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 |
|
| \(195\) |
\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 |
|
| \(196\) |
\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 |
|
| \(197\) |
\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 |
|
| \(198\) |
\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 |
|
| \(199\) |
\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 |
|
| \(200\) |
\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 |
|
| \(201\) |
\begin{align*}
x_{1}^{\prime }&=2 \sin \left (t \right ) x_{1}+\ln \left (t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{-2+t}+\frac {{\mathrm e}^{t} x_{2}}{1+t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (3\right ) &= 0 \\
x_{2} \left (3\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✓ |
0.056 |
|
| \(202\) |
\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 |
|
| \(203\) |
\begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(204\) |
\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 |
|
| \(205\) |
\begin{align*}
x^{\prime }&=y^{2}-x^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(206\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-\sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.039 |
|
| \(207\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 \sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.039 |
|
| \(208\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(209\) |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=\sin \left (x_{1}\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(210\) |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{1}^{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(211\) |
\begin{align*}
x^{\prime }&=5 x-6 y+x y \\
y^{\prime }&=6 x-7 y-x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(212\) |
\begin{align*}
x^{\prime }&=3 x-2 y+\left (x^{2}+y^{2}\right )^{2} \\
y^{\prime }&=4 x-y+\left (x^{2}-y^{2}\right )^{5} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.047 |
|
| \(213\) |
\begin{align*}
x^{\prime }&=y+x^{2}-x y \\
y^{\prime }&=-2 x+3 y+y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(214\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(215\) |
\begin{align*}
x^{\prime }&=-x-x^{2}+y^{2} \\
y^{\prime }&=-y+2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.046 |
|
| \(216\) |
\begin{align*}
x^{\prime }&=-2 x+y-x^{2}+2 y^{2} \\
y^{\prime }&=3 x+2 y+x^{2} y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.042 |
|
| \(217\) |
\begin{align*}
x^{\prime }&=-x+x^{2} \\
y^{\prime }&=-3 y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(218\) |
\begin{align*}
x^{\prime }&=-x+x y \\
y^{\prime }&=y+\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.042 |
|
| \(219\) |
\begin{align*}
x^{\prime }&=2 x+y^{2} \\
y^{\prime }&=3 y-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.041 |
|
| \(220\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(221\) |
\begin{align*}
y^{\prime }&=-2 \\
z^{\prime }&=x \,{\mathrm e}^{2 x +y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(222\) |
\begin{align*}
y y^{\prime }&=-x \\
y z^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.040 |
|
| \(223\) |
\begin{align*}
y^{\prime } x&=y \\
z^{\prime }&=3 y-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(224\) |
\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 |
|
| \(225\) |
\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 |
|
| \(226\) |
\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 |
|
| \(227\) |
\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 |
|
| \(228\) |
\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 |
|
| \(229\) |
\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 |
|
| \(230\) |
\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 |
|
| \(231\) |
\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 ) &= 10 \\
y_{1}^{\prime }\left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 10 \\
y_{2}^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.031 |
|
| \(232\) |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=y_{1} y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.039 |
|
| \(233\) |
\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 |
|
| \(234\) |
\begin{align*}
y_{1}^{\prime }&=t \sin \left (y_{1}\right )-y_{2} \\
y_{2}^{\prime }&=y_{1}+t \cos \left (y_{2}\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.051 |
|
| \(235\) |
\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 |
|
| \(236\) |
\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 |
|
| \(237\) |
\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 |
|
| \(238\) |
\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 |
|
| \(239\) |
\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 |
|
| \(240\) |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{2}}{t}+t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.051 |
|
| \(241\) |
\begin{align*}
y_{1}^{\prime }&=-\frac {y_{2}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {2 y_{2}}{t}-1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 2 \\
y_{2} \left (1\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.056 |
|
| \(242\) |
\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 |
|
| \(243\) |
\begin{align*}
y_{1}^{\prime }&=3 \sec \left (t \right ) y_{1}+5 \sec \left (t \right ) y_{2} \\
y_{2}^{\prime }&=-\sec \left (t \right ) y_{1}-3 \sec \left (t \right ) y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✓ |
0.057 |
|
| \(244\) |
\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 |
|
| \(245\) |
\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 |
|
| \(246\) |
\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 |
|
| \(247\) |
\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 |
|
| \(248\) |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.016 |
|
| \(249\) |
\begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(250\) |
\begin{align*}
x^{\prime }&=-2 x+y+x \,y^{2} \\
y^{\prime }&=-7 x-2 y-7 y \,x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(251\) |
\begin{align*}
x^{\prime }&=-y+x^{2} y^{3} \\
y^{\prime }&=x-x^{3} y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.027 |
|
| \(252\) |
\begin{align*}
x^{\prime }&=y+x^{3} \\
y^{\prime }&=x-y^{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.036 |
|
| \(253\) |
\begin{align*}
x^{\prime }&=-2 x+\sin \left (y\right ) \\
y^{\prime }&=5 \,{\mathrm e}^{x}-5-y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.040 |
|
| \(254\) |
\begin{align*}
x^{\prime }&=2 x-y \cos \left (y\right ) \\
y^{\prime }&=3 x-2 y-x \,y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.038 |
|