| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9601 |
\begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.489 |
|
| 9602 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 9603 |
\begin{align*}
4 y+y^{\prime \prime }&=x \left (\cos \left (x \right )+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 9604 |
\begin{align*}
4 y+y^{\prime \prime }&=x -4 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 9605 |
\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 \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9606 |
\begin{align*}
16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9607 |
\begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9608 |
\begin{align*}
6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| 9609 |
\begin{align*}
y^{\prime \prime }&=3 \sin \left (x \right )-4 y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9610 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| 9611 |
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.490 |
|
| 9612 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9613 |
\begin{align*}
2 y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\
y \left (1\right ) &= \frac {\sqrt {2}}{5} \\
y^{\prime }\left (1\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9614 |
\begin{align*}
x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| 9615 |
\begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 9 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9616 |
\begin{align*}
y^{\prime \prime }-y&=x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9617 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9618 | \begin{align*}
s^{\prime \prime }-3 s^{\prime }+2 s&=8 t^{2}+12 \,{\mathrm e}^{-t} \\
s \left (0\right ) &= 0 \\
s^{\prime }\left (0\right ) &= 2 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.490 |
|
| 9619 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 9620 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| 9621 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.491 |
|
| 9622 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9623 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 y p&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9624 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.491 |
|
| 9625 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9626 |
\begin{align*}
\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9627 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (x \right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9628 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9629 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=6 x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9630 |
\begin{align*}
x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\
-x+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9631 |
\begin{align*}
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 9632 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.491 |
|
| 9633 |
\begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 9634 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 9635 |
\(\left [\begin {array}{ccc} 2 & -2 & 0 \\ 2 & -2 & -1 \\ -2 & 2 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.492 |
|
| 9636 |
\begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (1\right ) &= -{\frac {1}{4}} \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 9637 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 9638 | \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=a x-2 y \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.492 |
|
| 9639 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \cos \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 9640 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 9641 |
\begin{align*}
y^{\prime \prime }+y&=10 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 9642 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9643 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9644 |
\begin{align*}
3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y&=\frac {4}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9645 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9646 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9647 |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9648 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9649 |
\begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.493 |
|
| 9650 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9651 |
\begin{align*}
2 x^{\prime }-y^{\prime }&=t \\
3 x^{\prime }+2 y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9652 |
\begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9653 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9654 |
\begin{align*}
y^{\prime \prime } x -3 y^{\prime } x +y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9655 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9656 |
\begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9657 | \begin{align*}
2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.493 |
|
| 9658 |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=-2 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 9659 |
\begin{align*}
4 y+y^{\prime \prime }&=3 x \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9660 |
\begin{align*}
x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9661 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9662 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9663 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.494 |
|
| 9664 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9665 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.494 |
|
| 9666 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 y+z \\
z^{\prime }&=z-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9667 |
\begin{align*}
\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9668 |
\begin{align*}
2 y^{\prime \prime }+9 y^{\prime } x -36 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9669 |
\begin{align*}
y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.494 |
|
| 9670 |
\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.494 |
|
| 9671 |
\begin{align*}
y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.494 |
|
| 9672 |
\begin{align*}
y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9673 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9674 |
\begin{align*}
y^{\prime \prime }&=y^{2} {\mathrm e}^{x}-{y^{\prime }}^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.494 |
|
| 9675 |
\begin{align*}
{y^{\prime }}^{2}-4 y^{\prime }+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| 9676 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.494 |
|
| 9677 | \begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.494 |
|
| 9678 |
\begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\
y \left (-1\right ) &= 1 \\
y^{\prime }\left (-1\right ) &= -1 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| 9679 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.495 |
|
| 9680 |
\begin{align*}
x^{\prime \prime }&=2 {x^{\prime }}^{3} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.495 |
|
| 9681 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| 9682 |
\begin{align*}
y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| 9683 |
\begin{align*}
N_{1}^{\prime }&=4 N_{1}-6 N_{2} \\
N_{2}^{\prime }&=8 N_{1}-10 N_{2} \\
\end{align*} With initial conditions \begin{align*}
N_{1} \left (0\right ) &= 100000 \\
N_{2} \left (0\right ) &= 1000 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| 9684 |
\begin{align*}
m y^{\prime \prime }+k y&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| 9685 |
\begin{align*}
1+y^{\prime }&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9686 |
\begin{align*}
9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9687 |
\begin{align*}
\left (1-x \right )^{2} x^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9688 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9689 |
\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.496 |
|
| 9690 |
\begin{align*}
y^{\prime }&=1-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9691 |
\begin{align*}
y^{\prime \prime }-4 y&=32 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9692 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9693 |
\begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=a x+\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9694 |
\begin{align*}
x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.496 |
|
| 9695 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=n^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9696 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| 9697 | \begin{align*}
4 y+y^{\prime \prime }&=3 x \cos \left (2 x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.497 |
|
| 9698 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{3} \\
x_{2}^{\prime }&=x_{2}-4 x_{3} \\
x_{3}^{\prime }&=x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| 9699 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| 9700 |
\begin{align*}
y^{\prime \prime \prime }&=2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.497 |
|