| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22701 |
\begin{align*}
r^{\prime }&=r^{2}+\frac {2 r}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.793 |
|
| 22702 |
\begin{align*}
y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.795 |
|
| 22703 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
7.795 |
|
| 22704 |
\begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.796 |
|
| 22705 |
\begin{align*}
y^{\prime }&=-x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.796 |
|
| 22706 |
\begin{align*}
x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.797 |
|
| 22707 |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
7.798 |
|
| 22708 |
\begin{align*}
\left (3 x +4 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.800 |
|
| 22709 |
\begin{align*}
\sin \left (x \right ) y^{2}+\left (\frac {1}{x}-\frac {y}{x}\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.800 |
|
| 22710 |
\begin{align*}
y^{\prime }&=y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.800 |
|
| 22711 |
\begin{align*}
y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 y a^{2} x^{4}+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 b^{2} x^{4} a +8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.803 |
|
| 22712 |
\begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.810 |
|
| 22713 |
\begin{align*}
y^{\prime }&=\frac {y+1}{x +2}-{\mathrm e}^{\frac {y+1}{x +2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.811 |
|
| 22714 |
\begin{align*}
y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.814 |
|
| 22715 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }&=4 y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.815 |
|
| 22716 |
\begin{align*}
x y^{\prime }+2 y&=6 x^{2} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.816 |
|
| 22717 |
\begin{align*}
\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.816 |
|
| 22718 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.816 |
|
| 22719 |
\begin{align*}
3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.821 |
|
| 22720 |
\begin{align*}
\left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.823 |
|
| 22721 |
\begin{align*}
x^{\prime }+x&=\operatorname {Heaviside}\left (t -a \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.824 |
|
| 22722 |
\begin{align*}
\left (2 \sin \left (y\right )-x \right ) y^{\prime }&=\tan \left (y\right ) \\
y \left (0\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.826 |
|
| 22723 |
\begin{align*}
\cos \left (x \right ) \cot \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.827 |
|
| 22724 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.829 |
|
| 22725 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
7.829 |
|
| 22726 |
\begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.833 |
|
| 22727 |
\begin{align*}
x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.841 |
|
| 22728 |
\begin{align*}
2 x y y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.844 |
|
| 22729 |
\begin{align*}
x y^{\prime \prime }+\left (a x +b +n \right ) y^{\prime }+n a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.844 |
|
| 22730 |
\begin{align*}
y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
7.848 |
|
| 22731 |
\begin{align*}
\left (3 x +3 y-4\right ) y^{\prime }&=-x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.849 |
|
| 22732 |
\begin{align*}
-2 y+\left (1-2 x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.851 |
|
| 22733 |
\begin{align*}
y^{\prime }+\frac {3 y}{x}&=6 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.851 |
|
| 22734 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
7.853 |
|
| 22735 |
\begin{align*}
x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.856 |
|
| 22736 |
\begin{align*}
3 x y^{\prime }&=\left (3 y^{3} \ln \left (x \right ) x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.857 |
|
| 22737 |
\begin{align*}
2 y y^{\prime \prime }&=3 y^{4}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.858 |
|
| 22738 |
\begin{align*}
a \,x^{2} \left (x -1\right )^{2} y^{\prime \prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.861 |
|
| 22739 |
\begin{align*}
2 y^{\prime }&=y^{3} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.861 |
|
| 22740 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=4 \cos \left (x \right )^{3} \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.862 |
|
| 22741 |
\begin{align*}
y^{\prime }&=\frac {1}{y}-\frac {y}{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.864 |
|
| 22742 |
\begin{align*}
x^{4} y^{\prime \prime }&=\left (-x y^{\prime }+y\right )^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.864 |
|
| 22743 |
\begin{align*}
2 y x -\tan \left (y\right )+\left (x^{2}-x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.867 |
|
| 22744 |
\begin{align*}
r^{\prime }&=\frac {r^{2}}{\theta } \\
r \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.868 |
|
| 22745 |
\begin{align*}
y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.873 |
|
| 22746 |
\begin{align*}
y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.878 |
|
| 22747 |
\begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.879 |
|
| 22748 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.881 |
|
| 22749 |
\begin{align*}
x^{3} y^{\prime }-\sin \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
7.881 |
|
| 22750 |
\begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.888 |
|
| 22751 |
\begin{align*}
x y^{\prime }&=2 x^{2} y+y \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.890 |
|
| 22752 |
\begin{align*}
y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.890 |
|
| 22753 |
\begin{align*}
\left (a +b \cos \left (2 x \right )+k \cos \left (4 x \right )\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
7.891 |
|
| 22754 |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.893 |
|
| 22755 |
\begin{align*}
2 x \left (y+2 \sqrt {x}\right ) y^{\prime }&=\left (y+\sqrt {x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.895 |
|
| 22756 |
\begin{align*}
3 x^{2}-2 y^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.895 |
|
| 22757 |
\begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.896 |
|
| 22758 |
\begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.897 |
|
| 22759 |
\begin{align*}
x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.898 |
|
| 22760 |
\begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.901 |
|
| 22761 |
\begin{align*}
y^{\prime }+y x&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.901 |
|
| 22762 |
\begin{align*}
2 y-3 t +t y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.910 |
|
| 22763 |
\begin{align*}
x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y&=\sin \left (x \right ) \cos \left (x \right )-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.911 |
|
| 22764 |
\begin{align*}
-y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.912 |
|
| 22765 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-y x -x^{2}-\frac {1}{x}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.912 |
|
| 22766 |
\begin{align*}
y y^{\prime }&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.912 |
|
| 22767 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right . \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
7.913 |
|
| 22768 |
\begin{align*}
t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.917 |
|
| 22769 |
\begin{align*}
y^{\prime }&=x y^{3}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
7.918 |
|
| 22770 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.919 |
|
| 22771 |
\begin{align*}
x y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+k y+a \,b^{2} x^{2 k} {\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.922 |
|
| 22772 |
\begin{align*}
x \left (-3+y\right ) y^{\prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.925 |
|
| 22773 |
\begin{align*}
x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.933 |
|
| 22774 |
\begin{align*}
t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N&=t \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.934 |
|
| 22775 |
\begin{align*}
\left (y+1\right ) y^{\prime }&=x \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.935 |
|
| 22776 |
\begin{align*}
y^{\prime }&=-\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.937 |
|
| 22777 |
\begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.938 |
|
| 22778 |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.939 |
|
| 22779 |
\begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.939 |
|
| 22780 |
\begin{align*}
y^{\prime }&=y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.940 |
|
| 22781 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+8 \left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.940 |
|
| 22782 |
\begin{align*}
y^{2} \left (x y^{\prime }+y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.941 |
|
| 22783 |
\begin{align*}
y^{\prime }&=\frac {\left (1+x y^{2}\right )^{2}}{y x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.942 |
|
| 22784 |
\begin{align*}
x y^{\prime }+y&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.943 |
|
| 22785 |
\begin{align*}
x^{\prime }&=\frac {x-t}{x-t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.944 |
|
| 22786 |
\begin{align*}
y^{\prime }&=\tan \left (6 x +3 y+1\right )-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.948 |
|
| 22787 |
\begin{align*}
x y^{\prime }+y&=\frac {1}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.951 |
|
| 22788 |
\begin{align*}
y^{\prime }&=\frac {y x +x +y^{2}}{\left (x -1\right ) \left (x +y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.951 |
|
| 22789 |
\begin{align*}
y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.953 |
|
| 22790 |
\begin{align*}
\left ({\mathrm e}^{y}+x +3\right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.954 |
|
| 22791 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.955 |
|
| 22792 |
\begin{align*}
\left (x y^{2}+x^{3}\right ) y^{\prime }&=2 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.957 |
|
| 22793 |
\begin{align*}
-y+y^{\prime }&=t y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.957 |
|
| 22794 |
\begin{align*}
i^{\prime }&=\frac {i t^{2}}{t^{3}-i^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.957 |
|
| 22795 |
\begin{align*}
y^{\prime }&=\tan \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.961 |
|
| 22796 |
\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*} |
✓ |
✓ |
✓ |
✗ |
7.967 |
|
| 22797 |
\begin{align*}
y^{\prime }&=\sqrt {a +b y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.970 |
|
| 22798 |
\begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
7.970 |
|
| 22799 |
\begin{align*}
y^{\prime }&=x^{3}+\frac {2 y}{x}-\frac {y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.971 |
|
| 22800 |
\begin{align*}
x^{3} y^{\prime }&=x^{2} \left (-1+y\right )+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.974 |
|