| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22501 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.386 |
|
| 22502 |
\begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.387 |
|
| 22503 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.388 |
|
| 22504 |
\begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+y x +2 x y^{2}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.388 |
|
| 22505 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (3\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.389 |
|
| 22506 |
\begin{align*}
\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.395 |
|
| 22507 |
\begin{align*}
y y^{\prime \prime }&=-a^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.396 |
|
| 22508 |
\begin{align*}
6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.400 |
|
| 22509 |
\begin{align*}
y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.401 |
|
| 22510 |
\begin{align*}
x&=t x^{\prime }-\ln \left (x^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.402 |
|
| 22511 |
\begin{align*}
\frac {2}{\sqrt {-x^{2}+1}}+y \cos \left (y x \right )+\left (x \cos \left (y x \right )-\frac {1}{y^{{1}/{3}}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
6.410 |
|
| 22512 |
\begin{align*}
x^{\prime }+\sec \left (t \right ) x&=\frac {1}{-1+t} \\
x \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.410 |
|
| 22513 |
\begin{align*}
y^{\prime }&=\frac {x +2 y}{x +2 y+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.412 |
|
| 22514 |
\begin{align*}
\sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=-\frac {\sin \left (x \right )^{2}}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.419 |
|
| 22515 |
\begin{align*}
x -y-2-\left (2 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.419 |
|
| 22516 |
\begin{align*}
y^{\prime } y-7 y&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.419 |
|
| 22517 |
\begin{align*}
3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.420 |
|
| 22518 | \begin{align*}
x^{2}+3 y^{2}-2 x y^{\prime } y&=0 \\
y \left (2\right ) &= 6 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 6.420 |
|
| 22519 |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.421 |
|
| 22520 |
\begin{align*}
y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right )}{x -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.421 |
|
| 22521 |
\begin{align*}
r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.421 |
|
| 22522 |
\begin{align*}
y^{\prime }&=x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.424 |
|
| 22523 |
\begin{align*}
\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.424 |
|
| 22524 |
\begin{align*}
x y^{\prime } y&=x^{2}-y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.434 |
|
| 22525 |
\begin{align*}
x^{\prime }&=\arctan \left (x\right )+t \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.441 |
|
| 22526 |
\begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.445 |
|
| 22527 |
\begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=2 x \left (\left (a^{2}+x^{2}\right )^{2}+3 y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.445 |
|
| 22528 |
\begin{align*}
y^{2}+x^{2}&=2 x y^{\prime } y \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.456 |
|
| 22529 |
\begin{align*}
2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.460 |
|
| 22530 |
\begin{align*}
y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.463 |
|
| 22531 |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} \sqrt {y^{2}+x^{2}}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.466 |
|
| 22532 |
\begin{align*}
y^{\prime }&=-\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-\textit {\_F1} \left (x \right )\right ) y}{\ln \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.467 |
|
| 22533 |
\begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.468 |
|
| 22534 |
\begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.469 |
|
| 22535 |
\begin{align*}
y^{\prime } y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.472 |
|
| 22536 |
\begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.474 |
|
| 22537 |
\begin{align*}
2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.475 |
|
| 22538 | \begin{align*}
y^{\prime \prime } x +\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y&=0 \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 6.476 |
|
| 22539 |
\begin{align*}
x -3 y&=\left (3 y-x +2\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.480 |
|
| 22540 |
\begin{align*}
y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x +y+y^{3}+y^{4}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.480 |
|
| 22541 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+x^{n} \left (b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.483 |
|
| 22542 |
\begin{align*}
y^{\prime } x&=a \,x^{n} y^{2}+b y+c \,x^{-n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.484 |
|
| 22543 |
\begin{align*}
{y^{\prime }}^{2}&=\left (y-1\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.491 |
|
| 22544 |
\begin{align*}
x^{2}+y^{2}+2 x y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.492 |
|
| 22545 |
\begin{align*}
y^{\prime }&=\frac {\left (\sqrt {y x +1}-1\right )^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.492 |
|
| 22546 |
\begin{align*}
y^{\prime }&=\left (3+x -4 y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.497 |
|
| 22547 |
\begin{align*}
y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.505 |
|
| 22548 |
\begin{align*}
y^{\prime }&=-\frac {\left (a \,x^{2}-2 F \left (y+\frac {a \,x^{4}}{8}\right )\right ) x}{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.510 |
|
| 22549 |
\begin{align*}
x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
6.514 |
|
| 22550 |
\begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.516 |
|
| 22551 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.516 |
|
| 22552 |
\begin{align*}
3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.517 |
|
| 22553 |
\begin{align*}
\left (1+5 x -y\right ) y^{\prime }+5+x -5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.517 |
|
| 22554 |
\begin{align*}
x&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.517 |
|
| 22555 |
\begin{align*}
x +2 y-4-\left (2 x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.517 |
|
| 22556 |
\begin{align*}
y^{\prime }&=t^{2} \tan \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.517 |
|
| 22557 | \begin{align*}
y^{\prime }&=\lambda \sinh \left (\lambda x \right ) y^{2}-\lambda \sinh \left (\lambda x \right )^{3} \\
\end{align*} | ✓ | ✓ | ✗ | ✗ | 6.521 |
|
| 22558 |
\begin{align*}
y^{\prime }&=y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.525 |
|
| 22559 |
\begin{align*}
y^{\prime }&=\frac {x}{-y+1+y^{4}+2 y^{2} x^{2}+x^{4}+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.535 |
|
| 22560 |
\begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.539 |
|
| 22561 |
\begin{align*}
3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.542 |
|
| 22562 |
\begin{align*}
x^{2} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.543 |
|
| 22563 |
\begin{align*}
y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.546 |
|
| 22564 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.551 |
|
| 22565 |
\begin{align*}
y^{\prime }&=\frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.554 |
|
| 22566 |
\begin{align*}
y^{\prime } x +y&=4 \sqrt {y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.555 |
|
| 22567 |
\begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.556 |
|
| 22568 |
\begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.556 |
|
| 22569 |
\begin{align*}
\cos \left (x \right ) y^{\prime }-y^{4}-y \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.565 |
|
| 22570 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.572 |
|
| 22571 |
\begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.577 |
|
| 22572 |
\begin{align*}
a \tan \left (\frac {x}{2}\right )^{2} y-\csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
6.579 |
|
| 22573 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.586 |
|
| 22574 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.592 |
|
| 22575 |
\begin{align*}
x^{2}-y^{2}+2 x y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.592 |
|
| 22576 | \begin{align*}
y^{\prime }&=y \left (a +b y^{2}\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 6.595 |
|
| 22577 |
\begin{align*}
y^{\prime }&=\sqrt {y+\sin \left (x \right )}-\cos \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
6.598 |
|
| 22578 |
\begin{align*}
y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.599 |
|
| 22579 |
\begin{align*}
x^{\prime }&=\sin \left (x\right )^{2} \cos \left (t \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.602 |
|
| 22580 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.603 |
|
| 22581 |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.609 |
|
| 22582 |
\begin{align*}
y^{\prime } y&=3 x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.617 |
|
| 22583 |
\begin{align*}
y^{\prime } x&=3 x^{2 n +1} y^{3}+\left (b x -n \right ) y+c \,x^{1-n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.617 |
|
| 22584 |
\begin{align*}
y^{\prime }&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.622 |
|
| 22585 |
\begin{align*}
x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.632 |
|
| 22586 |
\begin{align*}
x^{\prime }&=\frac {t^{2}}{1-x^{2}} \\
x \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.632 |
|
| 22587 |
\begin{align*}
y x +x^{2} y^{\prime }&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.632 |
|
| 22588 |
\begin{align*}
y^{\prime }&=\sqrt {y^{2}-1} \\
y \left (4\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.632 |
|
| 22589 |
\begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.635 |
|
| 22590 |
\begin{align*}
y^{\prime }&=\sqrt {a +b \cos \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.635 |
|
| 22591 |
\begin{align*}
y^{\prime }&=\frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.636 |
|
| 22592 |
\begin{align*}
\left (x +2 y+2\right ) y^{\prime }&=3 x -y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.636 |
|
| 22593 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (-1+k \right ) \left (\left (-a k +n \right ) x +m -b k \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
6.640 |
|
| 22594 |
\begin{align*}
y \left (1+\sqrt {1+x^{2} y^{4}}\right )+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.642 |
|
| 22595 | \begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \,x^{-n -2} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 6.651 |
|
| 22596 |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.652 |
|
| 22597 |
\begin{align*}
y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \\
\end{align*} |
✗ |
✗ |
✓ |
✓ |
6.652 |
|
| 22598 |
\begin{align*}
\left (2 y-6 x \right ) y^{\prime }-y+3 x +2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.655 |
|
| 22599 |
\begin{align*}
\left (-y+y^{\prime } x \right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.655 |
|
| 22600 |
\begin{align*}
3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.661 |
|