| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9901 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| 9902 |
\begin{align*}
x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| 9903 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| 9904 |
\begin{align*}
x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9905 |
\begin{align*}
\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9906 |
\begin{align*}
4 y+2 \left (1-2 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.510 |
|
| 9907 |
\begin{align*}
f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right )^{2} y^{\prime \prime }&=g \left (y, f \left (x \right ) y^{\prime }\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.510 |
|
| 9908 |
\begin{align*}
\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9909 |
\begin{align*}
\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9910 |
\begin{align*}
y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.510 |
|
| 9911 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9912 |
\begin{align*}
t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.510 |
|
| 9913 |
\begin{align*}
x {y^{\prime }}^{2}-2 y^{\prime } y-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9914 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y&=\cos \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9915 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{5 x} \\
y \left (0\right ) &= 12 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9916 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9917 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9918 | \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.510 |
|
| 9919 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+4 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9920 |
\begin{align*}
4 y^{\prime \prime }+y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9921 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.510 |
|
| 9922 |
\begin{align*}
{x^{\prime }}^{2}&=-4 x+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9923 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9924 |
\begin{align*}
i^{\prime \prime }+9 i&=12 \cos \left (3 t \right ) \\
i \left (0\right ) &= 4 \\
i^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9925 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| 9926 |
\begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| 9927 |
\begin{align*}
t y^{\prime \prime }+y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| 9928 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| 9929 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| 9930 |
\begin{align*}
4 y+y^{\prime \prime }&=2 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| 9931 |
\begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=2 x-5 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| 9932 |
\begin{align*}
y^{\prime \prime } x +\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.511 |
|
| 9933 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x}+{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| 9934 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\frac {1}{\left ({\mathrm e}^{x}-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.511 |
|
| 9935 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| 9936 |
\begin{align*}
1+y^{\prime }&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9937 | \begin{align*}
\left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.512 |
|
| 9938 |
\begin{align*}
f^{\prime \prime }+2 f^{\prime }+5 f&=0 \\
f \left (0\right ) &= 1 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9939 |
\begin{align*}
y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9940 |
\begin{align*}
3 x y^{2}+6 x^{2} y y^{\prime }+x^{3} {y^{\prime }}^{2}+x^{3} y y^{\prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.512 |
|
| 9941 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }+y \,{\mathrm e}^{t}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9942 |
\begin{align*}
\sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.512 |
|
| 9943 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9944 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9945 |
\begin{align*}
x {y^{\prime }}^{3}&=1+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9946 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9947 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9948 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }-x&=t^{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9949 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+4 y&={\mathrm e}^{x} \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| 9950 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9951 |
\begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9952 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9953 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=2 x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.513 |
|
| 9954 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9955 |
\begin{align*}
y^{\prime \prime }+\frac {\left (1-5 x \right ) y^{\prime }}{-x^{2}+x}-\frac {4 y}{-x^{2}+x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9956 | \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 x \sin \left (x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.513 |
|
| 9957 |
\begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9958 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9959 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.513 |
|
| 9960 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.513 |
|
| 9961 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.513 |
|
| 9962 |
\(\left [\begin {array}{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.513 |
|
| 9963 |
\begin{align*}
x {y^{\prime }}^{2}-2 y^{\prime } y-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9964 |
\begin{align*}
y&=y^{\prime } x +\frac {a}{{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.513 |
|
| 9965 |
\begin{align*}
y \left (y-2 y^{\prime } x \right )^{2}&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9966 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9967 |
\begin{align*}
4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9968 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=6 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9969 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9970 |
\begin{align*}
4 y+y^{\prime \prime }&=1-x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| 9971 |
\begin{align*}
x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| 9972 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| 9973 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| 9974 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=5 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| 9975 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x +1 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.514 |
|
| 9976 | \begin{align*}
x^{\prime }&=-5 x-2 y \\
y^{\prime }&=x-7 y \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.514 |
|
| 9977 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| 9978 |
\begin{align*}
3 t^{2} x-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| 9979 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x&=5 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| 9980 |
\begin{align*}
y^{\prime }&=3 y+12 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| 9981 |
\begin{align*}
y^{\prime }&=y-y^{2}-\frac {1}{4} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.514 |
|
| 9982 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 t}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| 9983 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.515 |
|
| 9984 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| 9985 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-a^{2} y^{\prime }+2 a^{2} y-\sinh \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| 9986 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.515 |
|
| 9987 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| 9988 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 9989 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 9990 |
\begin{align*}
y^{\prime \prime }+4 y&=t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 9991 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 9992 |
\begin{align*}
4 {y^{\prime }}^{3}+4 y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 9993 |
\begin{align*}
y^{\prime } y&=x +y^{2}-y^{2} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 9994 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+3 y^{\prime } x -8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 9995 | \begin{align*}
\left (y^{2}+x^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 0.516 |
|
| 9996 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 9997 |
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.516 |
|
| 9998 |
\begin{align*}
y^{\prime }&=x y^{3}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.516 |
|
| 9999 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=1-\delta \left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| 10000 |
\begin{align*}
x^{\prime }&=t +y \\
y^{\prime }&=-t +x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|