| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 11801 |
\begin{align*}
x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11802 |
\begin{align*}
y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.908 |
|
| 11803 |
\begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=6 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11804 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 11805 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{3}} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.909 |
|
| 11806 |
\begin{align*}
\left (a t +1\right ) y^{\prime }+y&=t \\
y \left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.909 |
|
| 11807 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| 11808 |
\begin{align*}
-\left (1-x \right ) y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.910 |
|
| 11809 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11810 |
\begin{align*}
x^{\prime }&=x+4 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11811 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11812 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11813 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11814 |
\begin{align*}
4 y+y^{\prime \prime }&=1-x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 11815 |
\begin{align*}
y^{\prime \prime }+y&=t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11816 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=3 x_{1}-4 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11817 |
\begin{align*}
\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11818 |
\begin{align*}
2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11819 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{\frac {x}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11820 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \csc \left (\frac {t}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11821 |
\begin{align*}
x^{\prime }+3 x+2 y&=0 \\
3 x+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 11822 |
\begin{align*}
\left ({\mathrm e}^{2 y}+x \right ) {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.912 |
|
| 11823 |
\begin{align*}
9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| 11824 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.912 |
|
| 11825 |
\begin{align*}
y^{\prime \prime }+\frac {\left (1-t \right ) y^{\prime }}{t}+\frac {\left (1-\cos \left (t \right )\right ) y}{t^{3}}&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.912 |
|
| 11826 |
\begin{align*}
x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 11827 |
\begin{align*}
x^{2} \left (4 x +1\right ) y^{\prime \prime }-x \left (1-4 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 11828 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 11829 |
\begin{align*}
\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 11830 |
\begin{align*}
b y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.913 |
|
| 11831 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11832 |
\begin{align*}
x^{\prime }&=x+3 z \\
y^{\prime }&=-y \\
z^{\prime }&=-3 x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11833 |
\begin{align*}
y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=A \cos \left (p x \right ) \\
y \left (0\right ) &= 9 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 11834 |
\begin{align*}
{y^{\prime }}^{3}&=b x +a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 11835 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 11836 |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {t^{2}+2 t}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 11837 |
\begin{align*}
y^{\prime }&=y+z+x \\
z^{\prime }&=1-y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 11838 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.916 |
|
| 11839 |
\begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| 11840 |
\begin{align*}
t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime }&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.916 |
|
| 11841 |
\begin{align*}
y^{\prime \prime \prime \prime }+y&=g \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11842 |
\begin{align*}
y^{\prime }+y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11843 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{2+x}+y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11844 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }&={\mathrm e}^{x}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.917 |
|
| 11845 |
\begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }-3 x&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11846 |
\begin{align*}
x^{\prime }-3 x-6 y&=27 t^{2} \\
x^{\prime }+y^{\prime }-3 y&=5 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11847 |
\begin{align*}
x^{4} {y^{\prime }}^{2}+2 y y^{\prime } x^{3}-4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11848 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11849 |
\begin{align*}
y^{\prime \prime } x +\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11850 |
\begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11851 |
\begin{align*}
r^{\prime }&=0 \\
r \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11852 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
z^{\prime }&=2 h \\
h^{\prime }&=-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 11853 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 11854 |
\begin{align*}
y^{\prime \prime } x +y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.919 |
|
| 11855 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=8 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.919 |
|
| 11856 |
\begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 11857 |
\begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 11858 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 11859 |
\begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11860 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11861 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11862 |
\begin{align*}
y^{\prime \prime } x +\left (-x^{2}+1\right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11863 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11864 |
\begin{align*}
\theta ^{\prime \prime }+4 \theta &=15 \cos \left (3 t \right ) \\
\theta \left (0\right ) &= 0 \\
\theta ^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11865 |
\begin{align*}
x^{\prime }&=7 x-y+6 z \\
y^{\prime }&=-10 x+4 y-12 z \\
z^{\prime }&=-2 x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11866 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{3} \\
x_{2}^{\prime }&=x_{2}-x_{3} \\
x_{3}^{\prime }&=-2 x_{1}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11867 |
\begin{align*}
4 x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11868 |
\begin{align*}
{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11869 |
\begin{align*}
\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11870 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.921 |
|
| 11871 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=1+2 x +3 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11872 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11873 |
\begin{align*}
y^{\prime \prime }&=\cos \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11874 |
\begin{align*}
\arctan \left (y x \right )+\frac {y x -2 x y^{2}}{y^{2} x^{2}+1}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{y^{2} x^{2}+1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| 11875 |
\begin{align*}
y_{1}^{\prime }&=2 y_{2} \\
y_{2}^{\prime }&=3 y_{1} \\
y_{3}^{\prime }&=2 y_{3}-y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11876 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| 11877 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11878 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\sqrt {1+t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| 11879 |
\begin{align*}
\left (1+y\right ) y^{\prime \prime }&={y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.923 |
|
| 11880 |
\begin{align*}
y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| 11881 |
\begin{align*}
x^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| 11882 |
\begin{align*}
2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11883 |
\begin{align*}
x^{\prime }-2 x+y&=0 \\
x+y^{\prime }-2 y&=-5 \,{\mathrm e}^{t} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11884 |
\begin{align*}
x^{4} y^{\prime \prime }&=-4 y^{2}+x \left (x^{2}+2 y\right ) y^{\prime } \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.924 |
|
| 11885 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11886 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11887 |
\begin{align*}
y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11888 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.924 |
|
| 11889 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.924 |
|
| 11890 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11891 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| 11892 |
\begin{align*}
y&=x^{2}+2 y^{\prime } x +\frac {{y^{\prime }}^{2}}{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.926 |
|
| 11893 |
\begin{align*}
x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| 11894 |
\begin{align*}
y^{\prime \prime }&=k \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| 11895 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| 11896 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=z-x \\
z^{\prime }&=x+3 y+z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| 11897 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| 11898 |
\begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| 11899 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.928 |
|
| 11900 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.928 |
|