| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 5501 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5502 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5503 |
\begin{align*}
\left (-y^{\prime } x +y\right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.436 |
|
| 5504 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5505 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.436 |
|
| 5506 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5507 |
\begin{align*}
{y^{\prime }}^{2}+\left (a x +b \right ) y^{\prime }-a y+c&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5508 |
\begin{align*}
x^{\prime }&=-5 x+3 y \\
y^{\prime }&=2 x-10 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5509 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5510 |
\begin{align*}
y^{\prime } x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5511 |
\begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5512 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } t -4 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 5513 |
\begin{align*}
y^{\prime }+y&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5514 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (4 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5515 |
\begin{align*}
a \,{\mathrm e}^{-1+y}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.437 |
|
| 5516 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
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. |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5517 |
\begin{align*}
x^{4} y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5518 |
\begin{align*}
x^{\prime }&=1-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5519 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5520 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=x_{1} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5521 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-3 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5522 |
\begin{align*}
y^{\prime }&=\frac {1}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5523 |
\begin{align*}
y_{1}^{\prime }-6 y_{1}&=-4 y_{2} \\
y_{2}^{\prime }&=2 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 5524 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5525 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\
x_{3}^{\prime }&=-2 x_{1}-4 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5526 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=g \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5527 |
\begin{align*}
{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5528 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5529 |
\begin{align*}
2 y y^{\prime \prime }&=-a^{2}-4 \left (-x^{2}+b \right ) y^{2}+8 x y^{3}+3 y^{4}+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.438 |
|
| 5530 |
\begin{align*}
y^{\prime \prime \prime \prime }&=\cos \left (x \right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5531 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5532 |
\begin{align*}
9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.438 |
|
| 5533 |
\begin{align*}
y^{\prime }&=3-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5534 |
\begin{align*}
\left (1-x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=5\). |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5535 |
\begin{align*}
y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.438 |
|
| 5536 |
\begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5537 |
\begin{align*}
y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5538 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-3 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 5539 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=2 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| 5540 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.439 |
|
| 5541 |
\begin{align*}
y^{\prime } x +y&=2 x^{4}+x^{3}+x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.439 |
|
| 5542 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.439 |
|
| 5543 |
\begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=-4 x+6 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| 5544 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| 5545 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| 5546 |
\begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| 5547 |
\begin{align*}
x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| 5548 |
\begin{align*}
y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| 5549 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| 5550 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| 5551 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| 5552 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.440 |
|
| 5553 |
\begin{align*}
x^{\prime }&=4 x+6 y \\
y^{\prime }&=-7 x-9 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| 5554 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +\lambda y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5555 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=2+x \\
y \left (0\right ) &= -{\frac {1}{3}} \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.441 |
|
| 5556 |
\begin{align*}
y^{\prime \prime }+y^{\prime } t +{\mathrm e}^{t} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5557 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5558 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5559 |
\begin{align*}
a y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.441 |
|
| 5560 |
\begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5561 |
\begin{align*}
\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.441 |
|
| 5562 |
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.441 |
|
| 5563 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5564 |
\begin{align*}
y^{\prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5565 |
\begin{align*}
y_{1}^{\prime }&=y_{2}-y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{3}-{\mathrm e}^{-t} \\
y_{3}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
y_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5566 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5567 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5568 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.441 |
|
| 5569 |
\begin{align*}
y^{\prime }+y&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5570 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| 5571 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5572 |
\begin{align*}
y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5573 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5574 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5575 |
\begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=-4 x+6 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5576 |
\begin{align*}
y^{\prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.442 |
|
| 5577 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5578 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=3 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5579 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 c x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5580 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.442 |
|
| 5581 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| 5582 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| 5583 |
\begin{align*}
x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| 5584 |
\begin{align*}
p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| 5585 |
\begin{align*}
x^{\prime }&=12 x-9 y \\
y^{\prime }&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| 5586 |
\begin{align*}
y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| 5587 |
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.443 |
|
| 5588 |
\begin{align*}
x^{\prime }&=\left (x-1\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.443 |
|
| 5589 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| 5590 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5591 |
\begin{align*}
y^{\prime }&=\left (1-y\right )^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5592 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5593 |
\begin{align*}
2 x^{\prime }+x-5 y^{\prime }-4 y&=0 \\
-y^{\prime }-2 x+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5594 |
\begin{align*}
\frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5595 |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5596 |
\begin{align*}
3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.444 |
|
| 5597 |
\begin{align*}
x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.444 |
|
| 5598 |
\begin{align*}
Q^{\prime }&=\frac {Q}{4+Q^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5599 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5600 |
\begin{align*}
x^{\prime }&=-9 y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|