| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10901 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10902 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=2-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10903 |
\begin{align*}
3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10904 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10905 |
\begin{align*}
9 y^{\prime \prime }-6 y^{\prime }+y&=\left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10906 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10907 |
\begin{align*}
x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10908 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10909 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+\left (x -\frac {4}{x}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10910 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+2 y+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10911 |
\begin{align*}
y^{\prime \prime }&=\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (1+a \right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| 10912 |
\begin{align*}
y^{\prime \prime }+y \ln \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10913 |
\begin{align*}
y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10914 |
\begin{align*}
4 y+y^{\prime \prime }&=\csc \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10915 |
\begin{align*}
y^{\prime } t +y&=t \\
y \left (1\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10916 |
\begin{align*}
x y^{\prime \prime \prime }+y^{\prime } x&=4 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10917 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10918 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10919 |
\begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.787 |
|
| 10920 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10921 |
\begin{align*}
y^{\prime \prime }+y&=8 x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10922 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10923 |
\begin{align*}
x^{\prime }&=x+2 y+t -1 \\
y^{\prime }&=3 x+2 y-5 t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10924 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10925 |
\begin{align*}
4 y y^{\prime }-4 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.788 |
|
| 10926 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}+6 y_{2}+6 y_{3} \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-4 y_{2}-3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10927 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10928 |
\begin{align*}
y^{\prime \prime }-\cos \left (x \right ) y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.788 |
|
| 10929 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left (x^{2}-1\right ) {\mathrm e}^{2 x}+\left (3 x +4\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10930 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\lambda \left (1+\lambda \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10931 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10932 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10933 |
\begin{align*}
2 y \left (x \,{\mathrm e}^{x^{2}}+\sin \left (x \right ) \cos \left (x \right ) y\right )+\left (2 \,{\mathrm e}^{x^{2}}+3 y \sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.789 |
|
| 10934 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10935 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10936 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10937 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10938 |
\begin{align*}
y^{\prime }&=\frac {\ln \left (x \right )}{x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10939 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y x&=\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.789 |
|
| 10940 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10941 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10942 |
\begin{align*}
-y+y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10943 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10944 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+4 t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 10945 |
\begin{align*}
4 x^{2} y^{\prime \prime }+3 y^{\prime } x +y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10946 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10947 |
\begin{align*}
y^{\prime \prime } x&=x {y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10948 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.790 |
|
| 10949 |
\begin{align*}
y^{\prime } t +y&=t \\
y \left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10950 |
\begin{align*}
x {y^{\prime }}^{3}&=1+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 10951 |
\begin{align*}
{\mathrm e}^{x} \sec \left (y\right )+\left ({\mathrm e}^{x}+1\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime }&=0 \\
y \left (3\right ) &= \frac {\pi }{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.790 |
|
| 10952 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10953 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+3 y&=x^{3}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10954 |
\begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.791 |
|
| 10955 |
\begin{align*}
x^{\prime }&=x+y-5 t +2 \\
y^{\prime }&=4 x-2 y-8 t -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10956 |
\begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10957 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.791 |
|
| 10958 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 10959 |
\begin{align*}
y^{\prime }&=-x +y \\
y \left (4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10960 |
\begin{align*}
y^{\prime \prime }+y&=x \cos \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10961 |
\begin{align*}
4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10962 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10963 |
\begin{align*}
y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10964 |
\begin{align*}
x \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 10965 |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10966 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+6 x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10967 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10968 |
\begin{align*}
y^{\prime }+4 \csc \left (x \right )&=\left (3-\cot \left (x \right )\right ) y+\sin \left (x \right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 10969 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 10970 |
\begin{align*}
x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10971 |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+b \,x^{n} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 10972 |
\begin{align*}
4 y+y^{\prime \prime }&=12 x^{2}-16 x \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10973 |
\begin{align*}
y^{\prime }&=2 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10974 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10975 |
\begin{align*}
3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10976 |
\begin{align*}
t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 10977 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10978 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10979 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 10980 |
\begin{align*}
x^{\prime }&=2 x-3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=x-2 y-\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10981 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=10 x_{1}+9 x_{2}+x_{3} \\
x_{3}^{\prime }&=-4 x_{1}-3 x_{2}+x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10982 |
\begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime \prime }+y^{\prime } x -n^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10983 |
\begin{align*}
\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10984 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.794 |
|
| 10985 |
\begin{align*}
\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 10986 |
\begin{align*}
{y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.794 |
|
| 10987 |
\begin{align*}
{y^{\prime }}^{3}-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.794 |
|
| 10988 |
\begin{align*}
y^{\prime \prime }+16 y&=\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10989 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10990 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 10991 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-x_{1} \\
x_{3}^{\prime }&=-x_{4} \\
x_{4}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10992 |
\begin{align*}
4 x^{3} y^{3}+\frac {1}{x}+\left (3 y^{2} x^{4}-\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10993 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10994 |
\begin{align*}
x^{\prime }&=2 x+3 y-7 \\
y^{\prime }&=-x-2 y+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10995 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10996 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10997 |
\begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 10998 |
\begin{align*}
\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| 10999 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 11000 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.797 |
|