| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 26701 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.864 |
|
| 26702 |
\begin{align*}
\frac {y^{2}-2 x^{2}}{-x^{3}+x y^{2}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.938 |
|
| 26703 |
\begin{align*}
y y^{\prime }&=\frac {y}{\left (a x +b \right )^{2}}+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.981 |
|
| 26704 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.019 |
|
| 26705 |
\begin{align*}
x^{2} {y^{\prime }}^{3}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
52.036 |
|
| 26706 |
\begin{align*}
\left (\cos \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \cos \left (\lambda x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.185 |
|
| 26707 |
\begin{align*}
-x y^{\prime }+y&=3 y^{2} y^{\prime } \\
y \left (3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.197 |
|
| 26708 |
\begin{align*}
y^{\prime }&=\frac {2 x -y}{2 x +y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.214 |
|
| 26709 |
\begin{align*}
\left (x^{2}+1\right ) \ln \left (x^{2}+1\right ) y^{\prime }-2 y x&=\ln \left (x^{2}+1\right )-2 x \arctan \left (x \right ) \\
y \left (-\infty \right ) &= -\frac {\pi }{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
52.217 |
|
| 26710 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.244 |
|
| 26711 |
\begin{align*}
2 y+\left (1-x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.325 |
|
| 26712 |
\begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.338 |
|
| 26713 |
\begin{align*}
x y^{\prime }-y&=x^{2} \sqrt {x^{2}-y^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.347 |
|
| 26714 |
\begin{align*}
\left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{-2+n} \left (b \,x^{m +1}+a n -a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
52.357 |
|
| 26715 |
\begin{align*}
\left (y x +1\right ) y-x \left (-y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.365 |
|
| 26716 |
\begin{align*}
x^{3}+2 x y^{2}-x +\left (x^{2} y+2 y^{3}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.439 |
|
| 26717 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right )^{3}&=a^{2} {y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.460 |
|
| 26718 |
\begin{align*}
\left (a x +b \right ) y^{\prime \prime }+s \left (c x +d \right ) y^{\prime }-s^{2} \left (\left (a +c \right ) x +b +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.504 |
|
| 26719 |
\begin{align*}
2 x -y+1+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.507 |
|
| 26720 |
\begin{align*}
y^{\prime }&=\sin \left (x +y\right )+\cos \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.549 |
|
| 26721 |
\begin{align*}
y&=x y^{\prime }+a x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.552 |
|
| 26722 |
\begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.586 |
|
| 26723 |
\begin{align*}
y&={y^{\prime }}^{2} x -2 {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.640 |
|
| 26724 |
\begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.658 |
|
| 26725 |
\begin{align*}
y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.680 |
|
| 26726 |
\begin{align*}
2 x -y-1+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.687 |
|
| 26727 |
\begin{align*}
\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.737 |
|
| 26728 |
\begin{align*}
3 x -y-5+\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.777 |
|
| 26729 |
\begin{align*}
{y^{\prime }}^{2} x^{2}-y \left (y-2 x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.779 |
|
| 26730 |
\begin{align*}
\left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
52.802 |
|
| 26731 |
\begin{align*}
y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
52.898 |
|
| 26732 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) y^{\prime \prime }+\left (a_{1} x +b_{1} \right ) y^{\prime }+\left (a_{0} x +b_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.931 |
|
| 26733 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.994 |
|
| 26734 |
\begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.152 |
|
| 26735 |
\begin{align*}
2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.202 |
|
| 26736 |
\begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.204 |
|
| 26737 |
\begin{align*}
\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.213 |
|
| 26738 |
\begin{align*}
2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \,x^{2}-c \right ) y^{\prime }+\lambda \,x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.249 |
|
| 26739 |
\begin{align*}
x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
53.254 |
|
| 26740 |
\begin{align*}
2 \sqrt {a y^{\prime }}+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.262 |
|
| 26741 |
\begin{align*}
y^{\prime \prime }-\frac {a^{2}}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.303 |
|
| 26742 |
\begin{align*}
x y^{\prime }-y+y^{2}&=x^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.305 |
|
| 26743 |
\begin{align*}
y^{\prime } \sqrt {b^{2}-x^{2}}&=\sqrt {a^{2}-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.338 |
|
| 26744 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\
x_{2}^{\prime }&=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\
x_{3}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\
x_{4}^{\prime }&=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\
x_{5}^{\prime }&=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.359 |
|
| 26745 |
\begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.450 |
|
| 26746 |
\begin{align*}
y^{\prime }&=t \sqrt {1-y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.563 |
|
| 26747 |
\begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.574 |
|
| 26748 |
\begin{align*}
\left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
53.603 |
|
| 26749 |
\begin{align*}
y^{\prime } \left (x^{2}+y^{2}+3\right )&=2 x \left (2 y-\frac {x^{2}}{y}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.610 |
|
| 26750 |
\begin{align*}
x y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
53.626 |
|
| 26751 |
\begin{align*}
2 x y^{\prime }-y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.631 |
|
| 26752 |
\begin{align*}
y^{2}-x^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.719 |
|
| 26753 |
\begin{align*}
y y^{\prime }-y&=A x +B \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.872 |
|
| 26754 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.872 |
|
| 26755 |
\begin{align*}
y^{\prime } \sqrt {b^{2}+x^{2}}&=\sqrt {y^{2}+a^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
53.987 |
|
| 26756 |
\begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
53.995 |
|
| 26757 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.034 |
|
| 26758 |
\begin{align*}
x^{\prime \prime }-x^{\prime }+x-x^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
54.038 |
|
| 26759 |
\begin{align*}
y^{\prime }&=\frac {2 x^{2}+y^{2}}{2 y x -x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.047 |
|
| 26760 |
\begin{align*}
12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.057 |
|
| 26761 |
\begin{align*}
y x +\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
54.107 |
|
| 26762 |
\begin{align*}
y^{\prime }&=\frac {\left (2 y \ln \left (x \right )-1\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
54.206 |
|
| 26763 |
\begin{align*}
\left (x -{y^{\prime }}^{2}\right ) y^{\prime \prime }&=x^{2}-y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
54.369 |
|
| 26764 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
54.415 |
|
| 26765 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
54.425 |
|
| 26766 |
\begin{align*}
3 y-7 x +7&=\left (3 x -7 y-3\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.477 |
|
| 26767 |
\begin{align*}
y+\left (2 x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.575 |
|
| 26768 |
\begin{align*}
y^{\prime }&=y^{{2}/{3}}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.648 |
|
| 26769 |
\begin{align*}
2 y x +\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
54.755 |
|
| 26770 |
\begin{align*}
x y^{\prime \prime }+2 x^{2} y^{\prime }+y \sin \left (x \right )&=\sinh \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
54.867 |
|
| 26771 |
\begin{align*}
R^{\prime \prime }&=-\frac {k}{R^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
54.960 |
|
| 26772 |
\begin{align*}
\left (x y^{\prime }+y\right )^{2}&=y^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
55.093 |
|
| 26773 |
\begin{align*}
t y^{\prime }&=y+\sqrt {t^{2}-y^{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
55.099 |
|
| 26774 |
\begin{align*}
\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+y^{3} b \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
55.118 |
|
| 26775 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
55.136 |
|
| 26776 |
\begin{align*}
2 x -3 y+\left (7 y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
55.146 |
|
| 26777 |
\begin{align*}
x^{3}+y^{3}+y^{2} \left (3 x +k y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
55.164 |
|
| 26778 |
\begin{align*}
y y^{\prime }+x&=a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
55.328 |
|
| 26779 |
\begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
55.444 |
|
| 26780 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\lambda x} y^{2}+a \,x^{n} y+a \lambda \,x^{n} {\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
55.463 |
|
| 26781 |
\begin{align*}
x \left (2-y x \right ) y^{\prime }+2 y-x y^{2} \left (y x +1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
55.773 |
|
| 26782 |
\begin{align*}
y^{\prime }&=-\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
55.773 |
|
| 26783 |
\begin{align*}
-\left (k -p \right ) \left (1+k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
55.819 |
|
| 26784 |
\begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
55.872 |
|
| 26785 |
\begin{align*}
{y^{\prime }}^{2}+\left (3 y-2 x \right ) y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
56.033 |
|
| 26786 |
\begin{align*}
y^{\prime }&=y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
56.072 |
|
| 26787 |
\begin{align*}
y^{\prime }&=-\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
56.125 |
|
| 26788 |
\begin{align*}
3 t y^{\prime }+9 y&=2 t y^{{5}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.161 |
|
| 26789 |
\begin{align*}
3 \sin \left (y\right )-5 x +2 x^{2} \cot \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.243 |
|
| 26790 |
\begin{align*}
y^{\prime } \sqrt {y x}+x -y&=\sqrt {y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
56.276 |
|
| 26791 |
\begin{align*}
\left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.342 |
|
| 26792 |
\begin{align*}
10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.347 |
|
| 26793 |
\begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.396 |
|
| 26794 |
\begin{align*}
6 y y^{\prime \prime }-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}&=36 {y^{\prime }}^{2} x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
56.477 |
|
| 26795 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=a^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.520 |
|
| 26796 |
\begin{align*}
\left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right )&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
56.595 |
|
| 26797 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.625 |
|
| 26798 |
\begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.648 |
|
| 26799 |
\begin{align*}
2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
56.664 |
|
| 26800 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
56.734 |
|