| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9901 |
\begin{align*}
8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.166 |
|
| 9902 |
\begin{align*}
2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.166 |
|
| 9903 |
\begin{align*}
y^{\prime }+a y&={\mathrm e}^{b t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.166 |
|
| 9904 |
\begin{align*}
2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.167 |
|
| 9905 |
\begin{align*}
5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.168 |
|
| 9906 |
\begin{align*}
x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| 9907 |
\begin{align*}
{y^{\prime }}^{2}&=\left (4 y+1\right ) \left (y^{\prime }-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.168 |
|
| 9908 |
\begin{align*}
y_{1}^{\prime }&=y_{1} \\
y_{2}^{\prime }&=2 y_{1}+y_{4} \\
y_{3}^{\prime }&=y_{4} \\
y_{4}^{\prime }&=y_{2}+2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| 9909 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.169 |
|
| 9910 |
\begin{align*}
t +y+1-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| 9911 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| 9912 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| 9913 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.172 |
|
| 9914 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.172 |
|
| 9915 |
\begin{align*}
3 y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.172 |
|
| 9916 |
\begin{align*}
2 y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.173 |
|
| 9917 |
\begin{align*}
y^{\prime \prime }+w^{2} y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.173 |
|
| 9918 |
\begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| 9919 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| 9920 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| 9921 |
\begin{align*}
x^{2} y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| 9922 |
\begin{align*}
y^{\prime \prime }&=2 \csc \left (x \right )^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.176 |
|
| 9923 |
\begin{align*}
y^{\prime \prime }+9 y&=8 \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= -1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| 9924 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| 9925 |
\begin{align*}
x^{\prime }&=x+2 y+z-w \\
y^{\prime }&=-y+2 z+2 w \\
z^{\prime }&=2 y+2 z+2 w \\
w^{\prime }&=-3 y-6 z-6 w \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| 9926 |
\begin{align*}
y^{\prime }&=a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| 9927 |
\begin{align*}
y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.177 |
|
| 9928 |
\begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.177 |
|
| 9929 |
\begin{align*}
u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.177 |
|
| 9930 |
\begin{align*}
y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.177 |
|
| 9931 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| 9932 |
\begin{align*}
t \left (1-t \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.179 |
|
| 9933 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| 9934 |
\begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.180 |
|
| 9935 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.180 |
|
| 9936 |
\begin{align*}
x^{\prime }&=-7 x+6 y+6 \,{\mathrm e}^{-t} \\
y^{\prime }&=-12 x+5 y+37 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.180 |
|
| 9937 |
\begin{align*}
y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.180 |
|
| 9938 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| 9939 |
\begin{align*}
2 y^{\prime \prime } x +\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| 9940 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| 9941 |
\begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| 9942 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| 9943 |
\begin{align*}
y^{\prime \prime }-y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| 9944 |
\begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| 9945 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| 9946 |
\begin{align*}
y^{\prime }&=y^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| 9947 |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.183 |
|
| 9948 |
\begin{align*}
4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.183 |
|
| 9949 |
\begin{align*}
{y^{\prime }}^{3}-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.183 |
|
| 9950 |
\begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| 9951 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=6 x_{2}-7 x_{3}+3 x_{4} \\
x_{3}^{\prime }&=3 x_{3}-x_{4} \\
x_{4}^{\prime }&=-4 x_{2}+9 x_{3}-3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| 9952 |
\begin{align*}
y^{\prime \prime }+y&=2 \sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| 9953 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| 9954 |
\begin{align*}
y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.184 |
|
| 9955 |
\begin{align*}
t y^{\prime \prime }+3 y&=t \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.184 |
|
| 9956 |
\begin{align*}
x^{2} \left (-y^{\prime } x +y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.184 |
|
| 9957 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| 9958 |
\begin{align*}
y^{\prime }&=y^{2}-3 y+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.185 |
|
| 9959 |
\begin{align*}
y^{\prime } x -3 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.186 |
|
| 9960 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.186 |
|
| 9961 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| 9962 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (2+x \right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.187 |
|
| 9963 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| 9964 |
\begin{align*}
4 x {y^{\prime }}^{2}-3 y y^{\prime }+3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.187 |
|
| 9965 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| 9966 |
\begin{align*}
4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.187 |
|
| 9967 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| 9968 |
\begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| 9969 |
\begin{align*}
y&=x^{6} {y^{\prime }}^{3}-y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.187 |
|
| 9970 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| 9971 |
\begin{align*}
2 y^{\prime }&=3 \left (y-2\right )^{{1}/{3}} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.188 |
|
| 9972 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| 9973 |
\begin{align*}
\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.188 |
|
| 9974 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| 9975 |
\begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=x+3 y \\
z^{\prime }&=2 z+w+h \\
w^{\prime }&=z+2 w+h \\
h^{\prime }&=z+w+2 h \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.189 |
|
| 9976 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{2}\right ) &= 0 \\
x^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.189 |
|
| 9977 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3}+12 t \\
x_{3}^{\prime }&=x_{1}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| 9978 |
\begin{align*}
4 t^{2} y^{\prime \prime }+y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| 9979 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| 9980 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| 9981 |
\begin{align*}
4 y^{\prime \prime } x +3 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| 9982 |
\begin{align*}
y^{\prime \prime }-y&=-20 \delta \left (t -3\right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.192 |
|
| 9983 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.193 |
|
| 9984 |
\begin{align*}
2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.193 |
|
| 9985 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.193 |
|
| 9986 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| 9987 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| 9988 |
\begin{align*}
2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.194 |
|
| 9989 |
\begin{align*}
x^{6} {y^{\prime }}^{3}-3 y^{\prime } x -3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.194 |
|
| 9990 |
\begin{align*}
t^{2} y+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.195 |
|
| 9991 |
\begin{align*}
y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.195 |
|
| 9992 |
\begin{align*}
2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.195 |
|
| 9993 |
\begin{align*}
2 t y+y^{\prime }&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.195 |
|
| 9994 |
\begin{align*}
x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.196 |
|
| 9995 |
\begin{align*}
b y+a y {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.196 |
|
| 9996 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.196 |
|
| 9997 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\
y \left (\pi \right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.196 |
|
| 9998 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\
x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| 9999 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+5 x_{2}+3 x_{3}-5 x_{4} \\
x_{2}^{\prime }&=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4} \\
x_{3}^{\prime }&=-x_{2}-2 x_{3}+x_{4} \\
x_{4}^{\prime }&=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| 10000 |
\begin{align*}
-y+2 y^{\prime } x +x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=2 x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.198 |
|