| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 20601 |
\begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.859 |
|
| 20602 |
\begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.861 |
|
| 20603 |
\begin{align*}
1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.862 |
|
| 20604 |
\begin{align*}
2 t -y^{2} \sin \left (y t \right )+\left (\cos \left (y t \right )-t y \sin \left (y t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.863 |
|
| 20605 |
\begin{align*}
\left (x -1\right ) y^{\prime }+3 y&=\frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.865 |
|
| 20606 |
\begin{align*}
y^{\prime }&=\cos \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.866 |
|
| 20607 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.867 |
|
| 20608 |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.868 |
|
| 20609 |
\begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.868 |
|
| 20610 |
\begin{align*}
\left (1-x \right ) y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.869 |
|
| 20611 |
\begin{align*}
y^{\prime \prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.870 |
|
| 20612 |
\begin{align*}
y&=t y^{\prime }+3 {y^{\prime }}^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.871 |
|
| 20613 |
\begin{align*}
y^{\prime }-a \sqrt {y}-b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.872 |
|
| 20614 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-a \,x^{2}+y^{2}\right )+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.872 |
|
| 20615 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.872 |
|
| 20616 |
\begin{align*}
z^{\prime \prime }+g z&=0 \\
z \left (\frac {\pi }{3 \sqrt {g}}\right ) &= 5 \\
z \left (\frac {2 \pi }{3 \sqrt {g}}\right ) &= \frac {\pi }{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.872 |
|
| 20617 |
\begin{align*}
2 \cos \left (x +y\right )-2 x \sin \left (x +y\right )-2 x \sin \left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.876 |
|
| 20618 |
\begin{align*}
y^{\prime }&=2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.877 |
|
| 20619 |
\begin{align*}
1+\sin \left (y\right )&=\left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.878 |
|
| 20620 |
\begin{align*}
y^{\prime }&=y \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| 20621 |
\begin{align*}
2 t \sin \left (y\right )-2 y \sin \left (t^{2}\right ) t +\left (\cos \left (y\right ) t^{2}+\cos \left (t^{2}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.879 |
|
| 20622 |
\begin{align*}
x -y+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| 20623 |
\begin{align*}
y^{\prime }&=\frac {y x +2 y}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| 20624 |
\begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.881 |
|
| 20625 |
\begin{align*}
5 y+{y^{\prime }}^{2}&=x \left (x +y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
4.885 |
|
| 20626 |
\begin{align*}
y^{\prime }&=y t \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.885 |
|
| 20627 |
\begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.886 |
|
| 20628 |
\begin{align*}
y^{\prime }&=-y^{2}+y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.886 |
|
| 20629 |
\begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.888 |
|
| 20630 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.889 |
|
| 20631 |
\begin{align*}
x^{4}+2 y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.891 |
|
| 20632 |
\begin{align*}
{y^{\prime \prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.892 |
|
| 20633 |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.893 |
|
| 20634 |
\begin{align*}
\ln \left (y^{x}\right ) y^{\prime }&=3 x^{2} y \\
y \left (2\right ) &= {\mathrm e}^{3} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
4.895 |
|
| 20635 |
\begin{align*}
y^{\prime }&=\left (x -y+3\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.896 |
|
| 20636 |
\begin{align*}
y^{\prime }&=-\frac {y}{t -2} \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.898 |
|
| 20637 |
\begin{align*}
x y y^{\prime }&=\left (x +1\right ) \left (y+1\right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.901 |
|
| 20638 |
\begin{align*}
1-{y^{\prime \prime }}^{2}+2 x y^{\prime \prime } y^{\prime \prime \prime }+\left (-x^{2}+1\right ) {y^{\prime \prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.901 |
|
| 20639 |
\begin{align*}
x y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.902 |
|
| 20640 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.902 |
|
| 20641 |
\begin{align*}
y^{\prime }-\frac {3 y}{2 x}&=6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.904 |
|
| 20642 |
\begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.905 |
|
| 20643 |
\begin{align*}
y^{\prime }&=\frac {-y x +1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.907 |
|
| 20644 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.910 |
|
| 20645 |
\begin{align*}
y^{\prime }&=3 x +y \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.910 |
|
| 20646 |
\begin{align*}
y y^{\prime \prime }&=-f \left (x \right ) y^{3}+y^{4}-f \left (x \right ) y^{\prime }+{y^{\prime }}^{2}+y f^{\prime \prime }\left (x \right ) \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
4.911 |
|
| 20647 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.913 |
|
| 20648 |
\begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.914 |
|
| 20649 |
\begin{align*}
y^{\prime \prime }&=\operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.914 |
|
| 20650 |
\begin{align*}
y+y \sqrt {x^{2} y^{4}+1}+2 x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.914 |
|
| 20651 |
\begin{align*}
\left (1-x^{2}+y^{2}\right ) y^{\prime }&=-y^{2}+x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.915 |
|
| 20652 |
\begin{align*}
4 t^{2} x^{\prime \prime }+8 x^{\prime } t +5 x&=0 \\
x \left (1\right ) &= 2 \\
x^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.919 |
|
| 20653 |
\begin{align*}
x y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.921 |
|
| 20654 |
\begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.922 |
|
| 20655 |
\begin{align*}
t y^{\prime }+m y&=t \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.923 |
|
| 20656 |
\begin{align*}
y^{\prime }&=\frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.924 |
|
| 20657 |
\begin{align*}
\left (1-x \right ) y^{\prime }+y x&=x \left (x -1\right )^{2} \\
y \left (5\right ) &= 24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.925 |
|
| 20658 |
\begin{align*}
2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.926 |
|
| 20659 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.926 |
|
| 20660 |
\begin{align*}
y^{\prime }+x y^{{1}/{3}}&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.929 |
|
| 20661 |
\begin{align*}
y^{\prime }&=-\frac {-2+y}{x -2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.931 |
|
| 20662 |
\begin{align*}
\frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.931 |
|
| 20663 |
\begin{align*}
x y^{\prime }&=x^{2}+y \left (y+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.934 |
|
| 20664 |
\begin{align*}
3 x y^{\prime }+5 y&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.934 |
|
| 20665 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+\left (n \,{\mathrm e}^{\lambda x}+m \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.936 |
|
| 20666 |
\begin{align*}
a x y^{3}+b y^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.938 |
|
| 20667 |
\begin{align*}
\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.939 |
|
| 20668 |
\begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \\
y \left (0\right ) &= -2^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.940 |
|
| 20669 |
\begin{align*}
2 x^{2} y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.941 |
|
| 20670 |
\begin{align*}
x \left (-x^{3}+1\right ) y^{\prime }&=x^{2}+\left (1-2 y x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.941 |
|
| 20671 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.943 |
|
| 20672 |
\begin{align*}
y^{\prime }&=y^{2}+b y+a \left (\lambda -b \right ) {\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.944 |
|
| 20673 |
\begin{align*}
\frac {x y^{\prime }}{y}&=\frac {2 y^{2}+1}{x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.945 |
|
| 20674 |
\begin{align*}
-a y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.946 |
|
| 20675 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.948 |
|
| 20676 |
\begin{align*}
n^{\prime }+n&=n t \,{\mathrm e}^{t +2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.948 |
|
| 20677 |
\begin{align*}
y^{\prime }-\tan \left (y\right )&=\frac {{\mathrm e}^{x}}{\cos \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.950 |
|
| 20678 |
\begin{align*}
y^{\prime }&=\frac {1}{-x +\left (\frac {1}{y}+1\right ) x +\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.951 |
|
| 20679 |
\begin{align*}
y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.953 |
|
| 20680 |
\begin{align*}
y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.953 |
|
| 20681 |
\begin{align*}
\left (1-x^{3}+6 x^{2} y^{2}\right ) y^{\prime }&=\left (6+3 y x -4 y^{3}\right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.954 |
|
| 20682 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\
y \left (2\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.954 |
|
| 20683 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.954 |
|
| 20684 |
\begin{align*}
2 y-8 x^{2}+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.954 |
|
| 20685 |
\begin{align*}
2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.957 |
|
| 20686 |
\begin{align*}
y^{\prime \prime }-k^{2} y&=0 \\
y \left (0\right ) &= v \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.957 |
|
| 20687 |
\begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-2 t}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.958 |
|
| 20688 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=-1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.959 |
|
| 20689 |
\begin{align*}
y y^{\prime }+t y^{2}&=t \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.959 |
|
| 20690 |
\begin{align*}
\left (x +y\right ) y^{\prime }+\tan \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.962 |
|
| 20691 |
\begin{align*}
\frac {1}{y}-\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.963 |
|
| 20692 |
\begin{align*}
y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.964 |
|
| 20693 |
\begin{align*}
y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.966 |
|
| 20694 |
\begin{align*}
2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (\cos \left (y\right ) t^{2}+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.967 |
|
| 20695 |
\begin{align*}
3 x^{2} y-x^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.967 |
|
| 20696 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+\lambda y-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.968 |
|
| 20697 |
\begin{align*}
1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.968 |
|
| 20698 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.968 |
|
| 20699 |
\begin{align*}
y^{\prime }&=2 y x -x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.969 |
|
| 20700 |
\begin{align*}
y y^{\prime }+2 {y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.970 |
|