| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 5801 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.464 |
|
| 5802 |
\begin{align*}
y^{\prime \prime }-y x&=1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.464 |
|
| 5803 |
\begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-t}}{\sqrt {t}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| 5804 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=4+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| 5805 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| 5806 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.464 |
|
| 5807 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=-x-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| 5808 |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+3 \left (x^{2}-3 x +2\right ) y^{\prime }+\left (x -2\right )^{2} x y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| 5809 |
\begin{align*}
y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+4 y&=0 \\
y \left (-2\right ) &= 1 \\
y^{\prime }\left (-2\right ) &= 0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| 5810 |
\begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=5 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| 5811 |
\begin{align*}
\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| 5812 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-5 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| 5813 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| 5814 |
\begin{align*}
-y+y^{\prime }&=t \,{\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| 5815 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| 5816 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+\frac {8}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| 5817 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| 5818 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| 5819 |
\begin{align*}
u^{\prime }-u^{2}&=\frac {2}{x^{{8}/{3}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.466 |
|
| 5820 |
\begin{align*}
\arctan \left (y x \right )+\frac {y x -2 x y^{2}}{1+y^{2} x^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+y^{2} x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.466 |
|
| 5821 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| 5822 |
\begin{align*}
x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| 5823 |
\begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| 5824 |
\begin{align*}
\sin \left (y^{\prime }\right )+y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.466 |
|
| 5825 |
\begin{align*}
-6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| 5826 |
\begin{align*}
y^{\prime \prime }-\left (x -3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| 5827 |
\begin{align*}
x_{1}^{\prime }&=-8 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-5 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| 5828 |
\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*} |
✗ |
✗ |
✗ |
✗ |
0.467 |
|
| 5829 |
\begin{align*}
a y^{\prime } \left (-y+y^{\prime } x \right )+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.467 |
|
| 5830 |
\begin{align*}
3 \left (1-y\right ) y y^{\prime \prime }&=2 \left (1-2 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.467 |
|
| 5831 |
\begin{align*}
x^{2} y y^{\prime \prime }&=-y^{2}+x^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.467 |
|
| 5832 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=4 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| 5833 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| 5834 |
\begin{align*}
\left (-3+y\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.467 |
|
| 5835 |
\begin{align*}
x^{\prime }&=-\frac {4 x}{5}+2 y \\
y^{\prime }&=-x+\frac {6 y}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| 5836 |
\begin{align*}
y&=y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.467 |
|
| 5837 |
\begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| 5838 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=t^{3} \cos \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| 5839 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| 5840 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| 5841 |
\begin{align*}
\left (a +x \right ) y^{\prime }&=b x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| 5842 |
\begin{align*}
y^{\prime \prime \prime }-y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| 5843 |
\begin{align*}
q^{\prime \prime }+9 q^{\prime }+14 q&=\frac {\sin \left (t \right )}{2} \\
q \left (0\right ) &= 0 \\
q^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| 5844 |
\begin{align*}
L i^{\prime }+R i&=E_{0} \operatorname {Heaviside}\left (t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.468 |
|
| 5845 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| 5846 |
\begin{align*}
y^{\prime \prime }+3 x^{3} y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| 5847 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| 5848 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| 5849 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| 5850 |
\begin{align*}
y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| 5851 |
\begin{align*}
y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| 5852 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3} \\
x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| 5853 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| 5854 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\
x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| 5855 |
\begin{align*}
y^{2}-\frac {y}{x \left (x +y\right )}+2+\left (\frac {1}{x +y}+2 \left (x +1\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.470 |
|
| 5856 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.470 |
|
| 5857 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.470 |
|
| 5858 |
\begin{align*}
x^{4} y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| 5859 |
\begin{align*}
x^{\prime }+3 x+4 y&=0 \\
y^{\prime }+2 x+5 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| 5860 |
\begin{align*}
x^{2} y^{\prime \prime \prime }+3 y^{\prime \prime } x +2 y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| 5861 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| 5862 |
\begin{align*}
x^{\prime }&=2 x+3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=-3 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| 5863 |
\begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=8 x_{1}-6 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| 5864 |
\begin{align*}
2 x y \,{\mathrm e}^{x^{2} y}+y^{2} {\mathrm e}^{x y^{2}}+1+\left (x^{2} {\mathrm e}^{x^{2} y}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.471 |
|
| 5865 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| 5866 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| 5867 |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| 5868 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (x^{3}+x y^{2}-y^{3}\right ) y^{\prime }+x^{3}-y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| 5869 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=12 x-7 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| 5870 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x -\left (3 x^{2}+2\right ) y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| 5871 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| 5872 |
\begin{align*}
x^{\prime }-3 x+2 y&=0 \\
y^{\prime }-x+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| 5873 |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| 5874 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| 5875 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime } x -\left (-x^{2}+3\right ) y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| 5876 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| 5877 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}-4 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| 5878 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| 5879 |
\begin{align*}
x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\
-x+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| 5880 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5881 |
\begin{align*}
x_{1}^{\prime }&=9 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-6 x_{1}-x_{2} \\
x_{3}^{\prime }&=6 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5882 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+5 x_{2}-5 x_{3} \\
x_{2}^{\prime }&=3 x_{1}-x_{2}+3 x_{3} \\
x_{3}^{\prime }&=8 x_{1}-8 x_{2}+10 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5883 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5884 |
\begin{align*}
y^{\prime \prime }-2 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.474 |
|
| 5885 |
\begin{align*}
y^{\prime } x +y&=\tan \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.474 |
|
| 5886 |
\begin{align*}
a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.474 |
|
| 5887 |
\begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.474 |
|
| 5888 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5889 |
\begin{align*}
y^{\prime \prime \prime }-12 y^{\prime }-16 y&={\mathrm e}^{4 t}-{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5890 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5891 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5892 |
\begin{align*}
y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| 5893 |
\begin{align*}
\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| 5894 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-7 x_{3} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| 5895 |
\begin{align*}
\frac {1}{x}+\frac {y^{\prime }}{y}+\frac {2}{y}-\frac {2 y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| 5896 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| 5897 |
\begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=-y \\
z^{\prime }&=4 z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| 5898 |
\begin{align*}
U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \\
\end{align*} Series expansion around \(r=0\). |
✓ |
✓ |
✓ |
✗ |
0.475 |
|
| 5899 |
\begin{align*}
t^{3} y^{\prime \prime }+\sin \left (t^{2}\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.476 |
|
| 5900 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.476 |
|