| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22601 |
\begin{align*}
x^{2} y^{\prime }&=\left (a x +y^{3} b \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.180 |
|
| 22602 |
\begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.184 |
|
| 22603 |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) x^{3} y\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.185 |
|
| 22604 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.198 |
|
| 22605 |
\begin{align*}
y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.205 |
|
| 22606 |
\begin{align*}
y^{\prime }&=\frac {2 x +y-1}{4 x +2 y+5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.206 |
|
| 22607 |
\begin{align*}
\left (A x y+B \,x^{2}+\left (-1+k \right ) A a y-\left (A b k +B a \right ) x \right ) y^{\prime }&=A y^{2}+B y x -\left (B a k +A b \right ) y+\left (-1+k \right ) B b x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.207 |
|
| 22608 |
\begin{align*}
3 x^{2} y^{3}-y^{2}+y+\left (-y x +2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.210 |
|
| 22609 |
\begin{align*}
\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.215 |
|
| 22610 |
\begin{align*}
y^{\prime } x +y&=\frac {1}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.215 |
|
| 22611 |
\begin{align*}
y y^{\prime } x&=x^{2}+2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.220 |
|
| 22612 |
\begin{align*}
\left (x -3 y+4\right ) y^{\prime }&=2 x -6 y+7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.222 |
|
| 22613 |
\begin{align*}
y^{\prime } x +y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.226 |
|
| 22614 |
\begin{align*}
y^{\prime }+\frac {3 y}{x}&=6 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.227 |
|
| 22615 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
11.228 |
|
| 22616 |
\begin{align*}
x +\left (2 x +3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.229 |
|
| 22617 |
\begin{align*}
y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.232 |
|
| 22618 |
\begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.232 |
|
| 22619 |
\begin{align*}
y^{\prime }&=-f^{\prime }\left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y-g \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
11.248 |
|
| 22620 |
\begin{align*}
-a \left (1+a \right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.252 |
|
| 22621 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.253 |
|
| 22622 |
\begin{align*}
y^{\prime }&=x^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.256 |
|
| 22623 |
\begin{align*}
y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.257 |
|
| 22624 |
\begin{align*}
y^{\prime }-2 \,{\mathrm e}^{x} y&=2 \sqrt {{\mathrm e}^{x} y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.263 |
|
| 22625 |
\begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.264 |
|
| 22626 |
\begin{align*}
\left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime }&=\frac {T}{t \sqrt {t^{2}-T^{2}}}-t \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.266 |
|
| 22627 |
\begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )-7 y x +7&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.272 |
|
| 22628 |
\begin{align*}
6 x -3 y+2-\left (2 x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.281 |
|
| 22629 |
\begin{align*}
y^{\prime }&=x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.283 |
|
| 22630 |
\begin{align*}
x \left (1-x^{2} y^{4}\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.284 |
|
| 22631 |
\begin{align*}
y^{\prime } x -\frac {y}{\ln \left (x \right )}&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.296 |
|
| 22632 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.301 |
|
| 22633 |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.302 |
|
| 22634 |
\begin{align*}
y^{\prime }+y^{2}&=\frac {a^{2}}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.303 |
|
| 22635 |
\begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.310 |
|
| 22636 |
\begin{align*}
\left (-x +y\right ) y^{\prime }+2 x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.315 |
|
| 22637 |
\begin{align*}
\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.319 |
|
| 22638 |
\begin{align*}
y^{\prime }&=\frac {y}{2 y \ln \left (y\right )+y-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.320 |
|
| 22639 |
\begin{align*}
x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.325 |
|
| 22640 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
11.325 |
|
| 22641 |
\begin{align*}
y^{\prime }&=\frac {\left (1+x y^{2}\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.326 |
|
| 22642 |
\begin{align*}
x +y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.328 |
|
| 22643 |
\begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.328 |
|
| 22644 |
\begin{align*}
x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.340 |
|
| 22645 |
\begin{align*}
y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.340 |
|
| 22646 |
\begin{align*}
\left (2+3 x -y x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.346 |
|
| 22647 |
\begin{align*}
y^{\prime } x -2 \sqrt {y x}&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.347 |
|
| 22648 |
\begin{align*}
\cos \left (x \right ) y-2 \sin \left (y\right )&=\left (2 x \cos \left (y\right )-\sin \left (x \right )\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.352 |
|
| 22649 |
\begin{align*}
y^{\prime }&=\frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.355 |
|
| 22650 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \operatorname {arccot}\left (x \right )^{n} y+\operatorname {arccot}\left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.359 |
|
| 22651 |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
11.360 |
|
| 22652 |
\begin{align*}
y y^{\prime }+x y^{2}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.362 |
|
| 22653 |
\begin{align*}
x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.365 |
|
| 22654 |
\begin{align*}
\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.367 |
|
| 22655 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+7 y&=\left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
11.376 |
|
| 22656 |
\begin{align*}
k&=\frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.378 |
|
| 22657 |
\begin{align*}
y^{2}+y y^{\prime } x&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.382 |
|
| 22658 |
\begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.393 |
|
| 22659 |
\begin{align*}
y^{\prime }&=\frac {4 y^{2}-x^{4}}{4 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.397 |
|
| 22660 |
\begin{align*}
y^{\prime }&=\sin \left (t -y\right )+\sin \left (y+t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.398 |
|
| 22661 |
\begin{align*}
2 x \sqrt {1-y^{2}}&=\left (x^{2}+1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.424 |
|
| 22662 |
\begin{align*}
y+\sqrt {x^{2}+y^{2}}-y^{\prime } x&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.434 |
|
| 22663 |
\begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.436 |
|
| 22664 |
\begin{align*}
t \left (s^{2}+t^{2}\right ) s^{\prime }-s \left (s^{2}-t^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.436 |
|
| 22665 |
\begin{align*}
-a y+\left (c -x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.454 |
|
| 22666 |
\begin{align*}
y^{\prime }&=2 x y \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.456 |
|
| 22667 |
\begin{align*}
\left (b \,x^{2}+a \right ) y+x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.484 |
|
| 22668 |
\begin{align*}
x +y-1+\left (2 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.484 |
|
| 22669 |
\begin{align*}
y^{\prime }&=y^{2}-4 \\
y \left (\frac {1}{4}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
11.487 |
|
| 22670 |
\begin{align*}
y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.494 |
|
| 22671 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{-2+n} y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
11.496 |
|
| 22672 |
\begin{align*}
\sec \left (x \right ) \cos \left (y\right )^{2}&=\cos \left (x \right ) \sin \left (y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.497 |
|
| 22673 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.499 |
|
| 22674 |
\begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.499 |
|
| 22675 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.502 |
|
| 22676 |
\begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.504 |
|
| 22677 |
\begin{align*}
\left (x +x \cos \left (y\right )\right ) y^{\prime }-\sin \left (y\right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.513 |
|
| 22678 |
\begin{align*}
-y+y^{\prime } x&=x^{2} y^{4} \left (y^{\prime } x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.514 |
|
| 22679 |
\begin{align*}
2 x -y \sin \left (2 x \right )&=\left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.519 |
|
| 22680 |
\begin{align*}
a \left (y^{\prime } x +2 y\right )&=y y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.519 |
|
| 22681 |
\begin{align*}
\left (x^{2}-y^{4}\right ) y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.521 |
|
| 22682 |
\begin{align*}
y^{\prime }&=\left (x -3\right ) \left (1+y\right )^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.522 |
|
| 22683 |
\begin{align*}
y^{\prime }&=\frac {x +2 y}{x +2 y+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.534 |
|
| 22684 |
\begin{align*}
\frac {2 t^{2} y \cos \left (t^{2}\right )-\sin \left (t^{2}\right ) y}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.534 |
|
| 22685 |
\begin{align*}
\left (y x +x \right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.536 |
|
| 22686 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.541 |
|
| 22687 |
\begin{align*}
y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.542 |
|
| 22688 |
\begin{align*}
y^{\prime }&=f^{\prime }\left (x \right ) y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.545 |
|
| 22689 |
\begin{align*}
y^{\prime }&=-\frac {y^{2} \left (x^{2} y-2 x -2 y x +y\right )}{2 \left (-2+y x -2 y\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.552 |
|
| 22690 |
\begin{align*}
y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{-x^{2}}+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.555 |
|
| 22691 |
\begin{align*}
y^{\prime }&=\frac {y-\sqrt {x^{2}+y^{2}}}{x} \\
y \left (3\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.556 |
|
| 22692 |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.556 |
|
| 22693 |
\begin{align*}
2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.558 |
|
| 22694 |
\begin{align*}
2 y^{\prime } x +4 y+a +\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.564 |
|
| 22695 |
\begin{align*}
r^{\prime } \left (1+\frac {\cos \left (\theta \right )}{2}\right )-r \sin \left (\theta \right )&=0 \\
r \left (\frac {\pi }{2}\right ) &= 2 a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.564 |
|
| 22696 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
11.574 |
|
| 22697 |
\begin{align*}
\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.582 |
|
| 22698 |
\begin{align*}
x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.584 |
|
| 22699 |
\begin{align*}
y^{\prime }-x \left (2+x \right ) y^{3}-\left (x +3\right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.586 |
|
| 22700 |
\begin{align*}
b y+\left (a +x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.588 |
|