| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19601 |
\begin{align*}
y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right ) y^{\prime }+\left (\frac {h^{\prime }\left (x \right ) \left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right )}{h \left (x \right )}-\frac {h^{\prime \prime }\left (x \right )}{h \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.852 |
|
| 19602 |
\begin{align*}
8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime }&=0 \\
y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.853 |
|
| 19603 |
\begin{align*}
y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.853 |
|
| 19604 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.855 |
|
| 19605 |
\begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.856 |
|
| 19606 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.858 |
|
| 19607 |
\begin{align*}
{\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.858 |
|
| 19608 |
\begin{align*}
y^{\prime \prime } x -2 \left (x -1\right ) y^{\prime }-y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.858 |
|
| 19609 |
\begin{align*}
y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| 19610 |
\begin{align*}
e y^{\prime \prime }&=\frac {P \left (\frac {L}{2}-x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| 19611 |
\begin{align*}
y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-\cot \left (x \right ) y&=\sin \left (x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.859 |
|
| 19612 |
\begin{align*}
2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.861 |
|
| 19613 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.861 |
|
| 19614 |
\begin{align*}
y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.861 |
|
| 19615 |
\begin{align*}
y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| 19616 |
\begin{align*}
y^{\prime } x +x +\tan \left (x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| 19617 |
\begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.862 |
|
| 19618 | \begin{align*}
y^{\prime }&=\frac {3 y+1}{x +3} \\
y \left (0\right ) &= 1 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.862 |
|
| 19619 |
\begin{align*}
p^{\prime }&=a p-b p^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| 19620 |
\begin{align*}
y^{\prime }&=\sqrt {1+6 x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.865 |
|
| 19621 |
\begin{align*}
2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.865 |
|
| 19622 |
\begin{align*}
t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.866 |
|
| 19623 |
\begin{align*}
x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\
y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\
z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.867 |
|
| 19624 |
\begin{align*}
y^{\prime }-2 y&=\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.867 |
|
| 19625 |
\begin{align*}
\left ({\mathrm e}^{x}+1\right ) y^{\prime }&=y-{\mathrm e}^{x} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.868 |
|
| 19626 |
\begin{align*}
2 y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.868 |
|
| 19627 |
\begin{align*}
y^{\prime } x&=2 x^{2} y+y \ln \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.868 |
|
| 19628 |
\begin{align*}
y^{2}-1+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.868 |
|
| 19629 |
\begin{align*}
3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.869 |
|
| 19630 |
\begin{align*}
y-\sin \left (x \right )^{2}+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.869 |
|
| 19631 |
\begin{align*}
r^{\prime \prime }&=\frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.871 |
|
| 19632 |
\begin{align*}
a {y^{\prime }}^{2}+y^{\prime } y-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.871 |
|
| 19633 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.871 |
|
| 19634 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.871 |
|
| 19635 |
\begin{align*}
y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.872 |
|
| 19636 |
\begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.872 |
|
| 19637 | \begin{align*}
x^{2} y+2 y^{4}+\left (x^{3}+3 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 2.872 |
|
| 19638 |
\begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+\left (-m^{2}+t^{2}\right ) x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✓ |
✓ |
2.873 |
|
| 19639 |
\begin{align*}
x +2 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.873 |
|
| 19640 |
\begin{align*}
\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.874 |
|
| 19641 |
\begin{align*}
\left (\ln \left (y\right )+x \right ) y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.874 |
|
| 19642 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.874 |
|
| 19643 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.874 |
|
| 19644 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {\left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )-\left (n +1\right ) x \operatorname {LegendreP}\left (n , x\right )}{x^{2}-1}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.875 |
|
| 19645 |
\begin{align*}
y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.876 |
|
| 19646 |
\begin{align*}
x \left (-x^{4}+1\right ) y^{\prime }&=2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.876 |
|
| 19647 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.878 |
|
| 19648 |
\begin{align*}
x^{2} y^{\prime }-y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.878 |
|
| 19649 |
\begin{align*}
2 y x +x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.879 |
|
| 19650 |
\begin{align*}
y^{\prime \prime }-\frac {a f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+b f \left (x \right )^{2 a} y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.879 |
|
| 19651 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.879 |
|
| 19652 |
\begin{align*}
y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.880 |
|
| 19653 |
\begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.880 |
|
| 19654 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.881 |
|
| 19655 |
\begin{align*}
x^{2} y^{\prime }+x y^{2}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.881 |
|
| 19656 |
\begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.882 |
|
| 19657 | \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.882 |
|
| 19658 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.886 |
|
| 19659 |
\begin{align*}
y+3 y^{\prime } x&=12 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.887 |
|
| 19660 |
\begin{align*}
y^{\prime }&=x^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.887 |
|
| 19661 |
\begin{align*}
{\mathrm e}^{x} y-2 x +{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.888 |
|
| 19662 |
\begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.888 |
|
| 19663 |
\begin{align*}
y^{\prime } x +\ln \left (x \right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.889 |
|
| 19664 |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.889 |
|
| 19665 |
\begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 t^{2} \operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 0 \\
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. |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| 19666 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| 19667 |
\begin{align*}
y^{\prime }&=\frac {x y}{x^{2}+1} \\
y \left (\sqrt {15}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| 19668 |
\begin{align*}
y&=y^{\prime } x +\arcsin \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.891 |
|
| 19669 |
\begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.892 |
|
| 19670 |
\begin{align*}
y^{\prime } y+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.893 |
|
| 19671 |
\begin{align*}
{\mathrm e}^{x} \left (x^{4} y^{2}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.894 |
|
| 19672 |
\begin{align*}
y^{\prime }&=2 x y^{2}+3 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.895 |
|
| 19673 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.895 |
|
| 19674 |
\begin{align*}
y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.896 |
|
| 19675 |
\begin{align*}
y^{\prime } x +2 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.897 |
|
| 19676 | \begin{align*}
y^{\prime } x +x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 2.897 |
|
| 19677 |
\begin{align*}
2 x y \cos \left (x^{2}\right )-2 y x +1+\left (\sin \left (x^{2}\right )-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.897 |
|
| 19678 |
\begin{align*}
y^{\prime }&=x^{2} \left (1+y\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| 19679 |
\begin{align*}
y^{\prime }&=-\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.898 |
|
| 19680 |
\begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.898 |
|
| 19681 |
\begin{align*}
2 y+3 x +y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.899 |
|
| 19682 |
\begin{align*}
y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.900 |
|
| 19683 |
\begin{align*}
2 y^{\prime }+a \,x^{2} {y^{\prime }}^{2}+y^{\prime \prime } x&=b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.900 |
|
| 19684 |
\begin{align*}
y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.900 |
|
| 19685 |
\begin{align*}
2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 y^{\prime } x -x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.901 |
|
| 19686 |
\begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.902 |
|
| 19687 |
\begin{align*}
y+x^{3}+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.902 |
|
| 19688 |
\begin{align*}
2 y^{\prime \prime }+18 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.905 |
|
| 19689 |
\begin{align*}
\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.908 |
|
| 19690 |
\begin{align*}
y^{\prime } x&=2 y+{\mathrm e}^{x} x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.908 |
|
| 19691 |
\begin{align*}
2 y \left (x^{2}-y+x \right )+\left (x^{2}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.908 |
|
| 19692 |
\begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.909 |
|
| 19693 |
\begin{align*}
x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.909 |
|
| 19694 |
\begin{align*}
y^{\prime } y&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.910 |
|
| 19695 | \begin{align*}
y^{\prime }&=5 \\
y \left (0\right ) &= 2 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.910 |
|
| 19696 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
2.912 |
|
| 19697 |
\begin{align*}
y-y^{\prime } x +\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.912 |
|
| 19698 |
\begin{align*}
y^{\prime }&=\frac {2 t}{y+t^{2} y} \\
y \left (2\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.913 |
|
| 19699 |
\begin{align*}
4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.913 |
|
| 19700 |
\begin{align*}
2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.914 |
|