| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8901 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 8902 |
\begin{align*}
y^{\prime \prime }-y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 8903 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 8904 |
\begin{align*}
y^{\prime \prime }+i y&=\cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 8905 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.584 |
|
| 8906 |
\begin{align*}
y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\
y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8907 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8908 |
\begin{align*}
y^{\prime \prime }-4 y&=100 \,{\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8909 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1} \\
x_{2}^{\prime }&=x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8910 |
\begin{align*}
4 y+y^{\prime \prime }&=2 \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8911 |
\begin{align*}
b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| 8912 |
\begin{align*}
2 y-3 x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8913 |
\begin{align*}
x^{\prime }&=4 x \\
y^{\prime }&=x-2 y \\
z^{\prime }&=x-4 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8914 |
\begin{align*}
x^{\prime \prime }+x&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8915 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8916 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8917 |
\begin{align*}
t y^{\prime \prime }+3 y&=t \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| 8918 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8919 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8920 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&={\mathrm e}^{2 x} \left (x +3\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 8921 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -2 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8922 |
\begin{align*}
\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8923 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8924 |
\begin{align*}
y^{\prime }&=1-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8925 |
\begin{align*}
y^{\prime } x&=-\sqrt {a^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8926 |
\begin{align*}
y^{\prime \prime }&=a +b x +c y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.586 |
|
| 8927 |
\begin{align*}
y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8928 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=x^{2}+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8929 |
\begin{align*}
x^{2} y^{\prime \prime }&=2 y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8930 |
\begin{align*}
y^{\prime \prime } x +v y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.586 |
|
| 8931 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8932 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8933 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8934 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8935 |
\begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8936 |
\begin{align*}
y^{\prime }&=3 \sin \left (x \right ) \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8937 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 8938 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| 8939 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.587 |
|
| 8940 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| 8941 |
\begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=a x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| 8942 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+4 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| 8943 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= -2 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| 8944 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8945 |
\begin{align*}
t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(t=1\). |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8946 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=t \,{\mathrm e}^{\alpha t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8947 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{2} \\
x_{3}^{\prime }&=-4 x_{1}-5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8948 |
\begin{align*}
-\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.588 |
|
| 8949 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+5 y&=40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8950 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8951 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8952 |
\begin{align*}
x^{\prime }&=-5 x+4 y \\
y^{\prime }&=2 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8953 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4 x +\sin \left (x \right )+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8954 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8955 |
\begin{align*}
2 y^{\prime }+y x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8956 |
\begin{align*}
y^{\prime \prime }+4 y&=F \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 8957 |
\begin{align*}
\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (1-4 x \right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8958 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=5 x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8959 |
\begin{align*}
2 x^{\prime }+x-5 y^{\prime }-4 y&=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right ) \\
3 x^{\prime }-2 x-4 y^{\prime }+y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8960 |
\begin{align*}
4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.589 |
|
| 8961 |
\begin{align*}
y^{\prime } x&=y x +y \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.589 |
|
| 8962 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8963 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8964 |
\begin{align*}
x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.589 |
|
| 8965 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8966 |
\begin{align*}
y^{\prime }+z^{\prime }+6 y&=0 \\
z^{\prime }+5 y+z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8967 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+3 \\
\end{align*} With initial conditions \begin{align*}
x \left (\pi \right ) &= 1 \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8968 |
\begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8969 |
\begin{align*}
y^{\prime \prime }+100 y&=\cos \left (\omega t \right )-\sin \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 8970 |
\begin{align*}
\left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8971 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-6 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+5 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8972 |
\begin{align*}
4 \left (-x +2\right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8973 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8974 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8975 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8976 |
\begin{align*}
y^{\prime } x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8977 |
\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.590 |
|
| 8978 |
\begin{align*}
y^{\prime }&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8979 |
\begin{align*}
y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8980 |
\begin{align*}
4 y+y^{\prime \prime }&=\tan \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8981 |
\begin{align*}
x_{1}^{\prime }&=a x_{1}+5 x_{3} \\
x_{2}^{\prime }&=-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8982 |
\begin{align*}
z^{\prime \prime }-3 z^{\prime }+z&=0 \\
z \left (0\right ) &= 1 \\
z^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 8983 |
\begin{align*}
x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.590 |
|
| 8984 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.590 |
|
| 8985 |
\begin{align*}
t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.590 |
|
| 8986 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=2 t^{2}+4 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 8987 |
\begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=8 x_{1}-6 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 8988 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 8989 |
\begin{align*}
x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.591 |
|
| 8990 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 8991 |
\begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 8992 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 8993 |
\begin{align*}
3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 8994 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 8995 |
\begin{align*}
x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 8996 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+9 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 8997 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.592 |
|
| 8998 |
\begin{align*}
\left (1+y\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -{\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.592 |
|
| 8999 |
\begin{align*}
y^{\prime }&=-4 x-y \\
x^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 9000 |
\begin{align*}
3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.592 |
|