| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18601 |
\begin{align*}
\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.815 |
|
| 18602 |
\begin{align*}
x^{2} y^{\prime }+2 x \left (1-x \right ) y&={\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.816 |
|
| 18603 |
\begin{align*}
\cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.817 |
|
| 18604 |
\begin{align*}
y^{\prime }-\frac {y}{t}&=\ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.818 |
|
| 18605 |
\begin{align*}
-\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.819 |
|
| 18606 |
\begin{align*}
y^{\prime }&=\frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.819 |
|
| 18607 |
\begin{align*}
y^{\prime } x&=x^{2} \sin \left (x \right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.820 |
|
| 18608 |
\begin{align*}
y \ln \left (y\right )-2 y x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.820 |
|
| 18609 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.820 |
|
| 18610 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=\frac {2}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.822 |
|
| 18611 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.825 |
|
| 18612 |
\begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.826 |
|
| 18613 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.828 |
|
| 18614 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=2 \cos \left (\ln \left (x +1\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.828 |
|
| 18615 |
\begin{align*}
3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.829 |
|
| 18616 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=-12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.829 |
|
| 18617 |
\begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\
y \left (\frac {1}{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.829 |
|
| 18618 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.829 |
|
| 18619 |
\begin{align*}
\csc \left (x \right ) \ln \left (y\right ) y^{\prime }+y^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.830 |
|
| 18620 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.830 |
|
| 18621 |
\begin{align*}
2 y y^{\prime } x +2 y^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.832 |
|
| 18622 |
\begin{align*}
\left (y x -1\right )^{2} x y^{\prime }+\left (y^{2} x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.832 |
|
| 18623 |
\begin{align*}
y^{\prime }-2 y x&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.832 |
|
| 18624 |
\begin{align*}
y^{\prime \prime }&=\frac {1+{y^{\prime }}^{2}}{2 y} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.833 |
|
| 18625 |
\begin{align*}
y^{\prime } x&=a y^{2}+b y+c \,x^{2 b} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.834 |
|
| 18626 |
\begin{align*}
y^{\prime } x&=y+x^{2} \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.834 |
|
| 18627 |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.835 |
|
| 18628 |
\begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.835 |
|
| 18629 |
\begin{align*}
\cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.836 |
|
| 18630 |
\begin{align*}
\left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+{\mathrm e}^{x} y&=2 x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.839 |
|
| 18631 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=x \tan \left (x \right )+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.839 |
|
| 18632 |
\begin{align*}
y^{\prime }-\frac {2 y}{t}&=t^{3} {\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.840 |
|
| 18633 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.840 |
|
| 18634 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.840 |
|
| 18635 |
\begin{align*}
x^{2}+y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.841 |
|
| 18636 |
\begin{align*}
\theta ^{\prime \prime }-p^{2} \theta &=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.841 |
|
| 18637 |
\begin{align*}
w^{3}+w z^{2}-z+\left (z^{3}+w^{2} z-w \right ) z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.841 |
|
| 18638 |
\begin{align*}
\frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.841 |
|
| 18639 |
\begin{align*}
3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.842 |
|
| 18640 |
\begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.842 |
|
| 18641 |
\begin{align*}
y y^{\prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.842 |
|
| 18642 |
\begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.842 |
|
| 18643 |
\begin{align*}
x {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.843 |
|
| 18644 |
\begin{align*}
y+1-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.843 |
|
| 18645 |
\begin{align*}
y^{\prime }&=-{\mathrm e}^{-t^{2}} y+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.844 |
|
| 18646 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\
x_{2}^{\prime }&=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\
x_{3}^{\prime }&=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\
x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+4 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.844 |
|
| 18647 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime }&=\left (1+y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.845 |
|
| 18648 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| 18649 |
\begin{align*}
\left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y&=\left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.846 |
|
| 18650 |
\begin{align*}
x^{\prime }+2 t x+t x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| 18651 |
\begin{align*}
-y+y^{\prime } x&=x \sqrt {x^{2}-y^{2}}\, y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.847 |
|
| 18652 |
\begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.847 |
|
| 18653 |
\begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| 18654 |
\begin{align*}
x^{4}+2 y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| 18655 |
\begin{align*}
y^{\prime } x +1&={\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| 18656 |
\begin{align*}
x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.849 |
|
| 18657 |
\begin{align*}
y^{\prime \prime }+y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.849 |
|
| 18658 |
\begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.852 |
|
| 18659 |
\begin{align*}
y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.852 |
|
| 18660 |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.853 |
|
| 18661 |
\begin{align*}
2 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.854 |
|
| 18662 |
\begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.856 |
|
| 18663 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.857 |
|
| 18664 |
\begin{align*}
y \cos \left (t \right )+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.860 |
|
| 18665 |
\begin{align*}
x^{\prime \prime }&=4 x^{3}-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.861 |
|
| 18666 |
\begin{align*}
y^{\prime }+7 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.862 |
|
| 18667 |
\begin{align*}
9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.864 |
|
| 18668 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=\sinh \left (x \right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.865 |
|
| 18669 |
\begin{align*}
{y^{\prime \prime \prime }}^{2}+x^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.865 |
|
| 18670 |
\begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.866 |
|
| 18671 |
\begin{align*}
3 t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.866 |
|
| 18672 |
\begin{align*}
\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.867 |
|
| 18673 |
\begin{align*}
y^{\prime } x +\left (2 x^{2}+1\right ) y&=x^{3} {\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.868 |
|
| 18674 |
\begin{align*}
\cos \left (\theta \right ) r^{\prime }&=2+2 r \sin \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.868 |
|
| 18675 |
\begin{align*}
x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.869 |
|
| 18676 |
\begin{align*}
2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.869 |
|
| 18677 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.870 |
|
| 18678 |
\begin{align*}
7 t^{2} x^{\prime }&=3 x-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.871 |
|
| 18679 |
\begin{align*}
2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.871 |
|
| 18680 |
\begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.873 |
|
| 18681 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.873 |
|
| 18682 |
\begin{align*}
4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.874 |
|
| 18683 |
\begin{align*}
y^{\prime }+y^{2}+k^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 18684 |
\begin{align*}
x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 18685 |
\begin{align*}
3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 18686 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (-2+t \right )+\delta \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.877 |
|
| 18687 |
\begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.878 |
|
| 18688 |
\begin{align*}
y^{\prime }&=2 t \cos \left (y\right )^{2} \\
y \left (0\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.878 |
|
| 18689 |
\begin{align*}
\cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.879 |
|
| 18690 |
\begin{align*}
-y^{\prime } x +y&=y^{\prime } y^{2} {\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.879 |
|
| 18691 |
\begin{align*}
-{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.880 |
|
| 18692 |
\begin{align*}
x^{\prime }&=\frac {y}{10} \\
y^{\prime }&=\frac {z}{5} \\
z^{\prime }&=\frac {2 x}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.880 |
|
| 18693 |
\begin{align*}
2 y-8 x^{2}+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.880 |
|
| 18694 |
\begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| 18695 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| 18696 |
\begin{align*}
3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.882 |
|
| 18697 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| 18698 |
\begin{align*}
y^{\prime } x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.883 |
|
| 18699 |
\begin{align*}
t^{2} y^{\prime \prime }-5 y^{\prime } t +5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.884 |
|
| 18700 |
\begin{align*}
y^{\prime }+x \left (-x +y\right )+x^{3} \left (-x +y\right )^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.884 |
|