| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 6801 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=f \left (t \right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| 6802 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| 6803 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| 6804 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.583 |
|
| 6805 |
\begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| 6806 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.583 |
|
| 6807 |
\begin{align*}
x^{\prime }&=3 x-y+1 \\
y^{\prime }&=x+y+2 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| 6808 |
\begin{align*}
x^{\prime }&=-4 x+2 y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| 6809 |
\begin{align*}
x^{\prime }&=-3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| 6810 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=-4 x_{1}+x_{2} \\
x_{3}^{\prime }&=3 x_{1}+6 x_{2}+2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= -30 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 6811 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 6812 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.584 |
|
| 6813 |
\begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.584 |
|
| 6814 |
\begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 6815 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-4 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 6816 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 6817 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.584 |
|
| 6818 |
\begin{align*}
\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.584 |
|
| 6819 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 6820 |
\begin{align*}
x^{\prime }+3 x-y^{\prime }-y&=0 \\
2 x^{\prime }-9 x+y^{\prime }+4 y&=15 \,{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| 6821 |
\begin{align*}
y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| 6822 |
\begin{align*}
f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| 6823 |
\begin{align*}
2 y y^{\prime \prime }&=8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.585 |
|
| 6824 |
\begin{align*}
y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 6825 |
\begin{align*}
\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 6826 |
\begin{align*}
5 x^{\prime }-3 y^{\prime }&=x+y \\
3 x^{\prime }-y^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 6827 |
\begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 6828 |
\begin{align*}
y_{1}^{\prime }&=y_{2}+t \\
y_{2}^{\prime }&=-y_{1}-t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| 6829 |
\begin{align*}
\left (3 x^{2}+1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 6830 |
\begin{align*}
9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 6831 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 6832 |
\begin{align*}
x^{\prime }&=z \\
y^{\prime }&=y \\
z^{\prime }&=x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 6833 |
\begin{align*}
\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 6834 |
\begin{align*}
y^{\prime }&=\sin \left (2 t \right )-\cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 6835 |
\begin{align*}
x \left (x^{2}-4\right ) y^{\prime }&=1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| 6836 |
\begin{align*}
x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.586 |
|
| 6837 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}+{\mathrm e}^{t} \\
y_{2}^{\prime }&=y_{1}+2 y_{2}-{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.586 |
|
| 6838 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x^{2} y^{\prime }+\left (-5 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| 6839 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=2 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| 6840 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| 6841 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-v^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.588 |
|
| 6842 |
\begin{align*}
t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.588 |
|
| 6843 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=12 x \sin \left (x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 6844 |
\begin{align*}
x^{\prime }&=3 x+y-z \\
y^{\prime }&=x+3 y-z \\
z^{\prime }&=3 x+3 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 6845 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 6846 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| 6847 |
\begin{align*}
y^{\prime }&=y-y^{2}-\frac {1}{4} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.588 |
|
| 6848 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6849 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\
x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6850 |
\begin{align*}
\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (x -1\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6851 |
\begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y&={\mathrm e}^{x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6852 |
\begin{align*}
y^{\prime \prime }&=\operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.589 |
|
| 6853 |
\begin{align*}
y^{\prime }&=y^{2}-y-6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6854 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.589 |
|
| 6855 |
\begin{align*}
x^{\prime }&=-x+4 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6856 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.589 |
|
| 6857 |
\begin{align*}
2 y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6858 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6859 |
\begin{align*}
x^{\prime }&=-3 x-5 y \\
y^{\prime }&=3 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6860 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x -8 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6861 |
\begin{align*}
y&=2 y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.589 |
|
| 6862 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6863 |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{2}-y_{2}+5 \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{2}-5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| 6864 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}-2 \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 6865 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 6866 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 6867 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.590 |
|
| 6868 |
\begin{align*}
x^{\prime }&=2 x+4 y+\cos \left (t \right ) \\
y^{\prime }&=-x-2 y+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| 6869 |
\begin{align*}
x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.591 |
|
| 6870 |
\begin{align*}
\left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 6871 |
\begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 6872 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 6873 |
\begin{align*}
t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 6874 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.591 |
|
| 6875 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.591 |
|
| 6876 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 6877 |
\begin{align*}
y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 6878 |
\begin{align*}
t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| 6879 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+9 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6880 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6881 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \sin \left (2 x \right ) {\mathrm e}^{x}-10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6882 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=30 \cos \left (x \right )-10 \sin \left (x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
y^{\prime \prime }\left (0\right ) &= 16 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6883 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6884 |
\begin{align*}
y^{\prime \prime \prime }&=x^{2}+\sin \left (x \right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6885 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=5 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6886 |
\begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.592 |
|
| 6887 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6888 |
\begin{align*}
8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6889 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }-3 y^{\prime }+\left (x -1\right ) y&=0 \\
y \left (1\right ) &= -20 \\
y^{\prime }\left (1\right ) &= -2 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 6890 |
\begin{align*}
\left (3 x^{2}+2 x +1\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 6891 |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=f \left (x \right ) \left (1-y\right ) y y^{\prime }+\left (1-2 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.593 |
|
| 6892 |
\begin{align*}
x^{\prime }&=4 x-5 y \\
y^{\prime }&=5 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 6893 |
\begin{align*}
x \sin \left (x \right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 6894 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 6895 |
\begin{align*}
y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 6896 |
\begin{align*}
x^{\prime }&=x+5 y \\
y^{\prime }&=-x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 6897 |
\begin{align*}
x^{\prime }&=y+z-x \\
y^{\prime }&=x-y+z \\
z^{\prime }&=x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 6898 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.594 |
|
| 6899 |
\begin{align*}
y^{\prime \prime }+\left (3 x^{2}+12 x +13\right ) y^{\prime }+\left (5+2 x \right ) y&=0 \\
y \left (-2\right ) &= 2 \\
y^{\prime }\left (-2\right ) &= -3 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 6900 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|