| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12801 |
\begin{align*}
x^{2}-2 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.225 |
|
| 12802 |
\begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.225 |
|
| 12803 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 12804 |
\begin{align*}
y^{\prime \prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 12805 |
\begin{align*}
y^{\prime }-\frac {6 y}{x}&=7 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 12806 |
\begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 12807 |
\begin{align*}
y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| 12808 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=\alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| 12809 |
\begin{align*}
y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 12810 |
\begin{align*}
y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.228 |
|
| 12811 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.228 |
|
| 12812 |
\begin{align*}
y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.228 |
|
| 12813 |
\begin{align*}
u^{\prime \prime }+\left (\tan \left (x \right )-2 \cos \left (x \right )\right ) u^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.228 |
|
| 12814 |
\begin{align*}
y^{\prime }&=8 y x +3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.228 |
|
| 12815 |
\begin{align*}
y^{\prime } x +n y&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 12816 |
\begin{align*}
y^{\prime }+2 x y \left (1-a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 12817 |
\begin{align*}
4 x^{2} y^{\prime \prime }+y&=8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 12818 |
\begin{align*}
y^{\prime }&=\cot \left (x \right ) y+\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 12819 |
\begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 12820 |
\begin{align*}
\frac {y}{t}+y^{\prime }&=5+\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 12821 |
\begin{align*}
y \left (x +y+1\right )+x \left (x +3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.232 |
|
| 12822 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| 12823 |
\begin{align*}
\frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.233 |
|
| 12824 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.233 |
|
| 12825 |
\begin{align*}
\left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.234 |
|
| 12826 |
\begin{align*}
s^{\prime \prime }&=5 t^{2}-7 t \\
s \left (0\right ) &= 0 \\
s \left (1\right ) &= {\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| 12827 |
\begin{align*}
\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+{\mathrm e}^{x} y+{\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.235 |
|
| 12828 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.235 |
|
| 12829 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.235 |
|
| 12830 |
\begin{align*}
y^{\prime }&=\frac {3 y}{t}+t^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.235 |
|
| 12831 |
\begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.235 |
|
| 12832 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.236 |
|
| 12833 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| 12834 |
\begin{align*}
\left (1-x^{3}+6 y^{2} x^{2}\right ) y^{\prime }&=\left (6+3 y x -4 y^{3}\right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.238 |
|
| 12835 |
\begin{align*}
y \left (2 y^{2}+1\right ) y^{\prime }&=x \left (2 x^{2}+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.238 |
|
| 12836 |
\begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.239 |
|
| 12837 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.239 |
|
| 12838 |
\begin{align*}
\left (x +1\right ) y^{\prime }-y^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| 12839 |
\begin{align*}
x \left (3-2 x^{2} y\right ) y^{\prime }&=4 x -3 y+3 y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.240 |
|
| 12840 |
\begin{align*}
\left (-2+2 y\right ) y^{\prime }&=3 x^{2}+4 x +2 \\
y \left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| 12841 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| 12842 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| 12843 |
\begin{align*}
y^{\prime }&=\frac {y}{1+t}+10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| 12844 |
\begin{align*}
y^{\prime } x +y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.241 |
|
| 12845 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.241 |
|
| 12846 |
\begin{align*}
r^{\prime }+r \sec \left (t \right )&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.241 |
|
| 12847 |
\begin{align*}
y^{\prime }&=\cot \left (x \right ) y+\csc \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.241 |
|
| 12848 |
\begin{align*}
y^{\prime }&=-\frac {i \left (i x +1+x^{4}+2 y^{2} x^{2}+y^{4}+x^{6}+3 y^{2} x^{4}+3 x^{2} y^{4}+y^{6}\right )}{y} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.242 |
|
| 12849 |
\begin{align*}
y^{\prime }&=\frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| 12850 |
\begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| 12851 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| 12852 |
\begin{align*}
x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\
x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\
x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| 12853 |
\begin{align*}
y^{\prime }&=\sin \left (2 x \right )-\tan \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| 12854 |
\begin{align*}
3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.243 |
|
| 12855 |
\begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| 12856 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| 12857 |
\begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| 12858 |
\begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{3} \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| 12859 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= -1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| 12860 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.245 |
|
| 12861 |
\begin{align*}
\left (x^{2}+1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.246 |
|
| 12862 |
\begin{align*}
-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.246 |
|
| 12863 |
\begin{align*}
-\left (n \left (n -1\right )-a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| 12864 |
\begin{align*}
x^{\prime }&=a_{1} x+b_{1} y+c_{1} \\
y^{\prime }&=a_{2} x+b_{2} y+c_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| 12865 |
\begin{align*}
x^{\prime \prime }+x&=\frac {1}{1+t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| 12866 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.248 |
|
| 12867 |
\begin{align*}
y^{\prime }&=-\frac {y}{1+t}+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.248 |
|
| 12868 |
\begin{align*}
y^{\prime }&=\frac {x}{x^{2} y+y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.248 |
|
| 12869 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{2} \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.248 |
|
| 12870 |
\begin{align*}
y^{\prime }&=t y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.248 |
|
| 12871 |
\begin{align*}
\left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.249 |
|
| 12872 |
\begin{align*}
y^{\prime \prime }+\frac {y}{4 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| 12873 |
\begin{align*}
y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| 12874 |
\begin{align*}
x^{2} y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.251 |
|
| 12875 |
\begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.252 |
|
| 12876 |
\begin{align*}
y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.252 |
|
| 12877 |
\begin{align*}
y^{\prime }&=\frac {x^{2}-2 x^{2} y+2}{x^{3}} \\
y \left (1\right ) &= {\frac {3}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.253 |
|
| 12878 |
\begin{align*}
y^{\prime }&=\sin \left (x \right )+2 \tan \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.253 |
|
| 12879 |
\begin{align*}
y^{\prime \prime }-\frac {2 y}{x^{2}}&=x \,{\mathrm e}^{-\sqrt {x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.253 |
|
| 12880 |
\begin{align*}
y^{\prime }&=\frac {a x +b}{y^{n}+d} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.253 |
|
| 12881 |
\begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.254 |
|
| 12882 |
\begin{align*}
y^{\prime }&=t^{4} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.254 |
|
| 12883 |
\begin{align*}
16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| 12884 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.255 |
|
| 12885 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| 12886 |
\begin{align*}
-x^{\prime \prime }+x&={\mathrm e}^{-x} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.255 |
|
| 12887 |
\begin{align*}
y^{\prime }&=2 y x \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.256 |
|
| 12888 |
\begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.257 |
|
| 12889 |
\begin{align*}
y^{\prime }&=x^{2} \left (1+y\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.258 |
|
| 12890 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.258 |
|
| 12891 |
\begin{align*}
y^{\prime }&=a \sin \left (b x +c \right )+k y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| 12892 |
\begin{align*}
y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y&=\frac {1}{-x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.260 |
|
| 12893 |
\begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.260 |
|
| 12894 |
\begin{align*}
{\mathrm e}^{t} x+1+\left ({\mathrm e}^{t}-1\right ) x^{\prime }&=0 \\
x \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.262 |
|
| 12895 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.262 |
|
| 12896 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| 12897 |
\begin{align*}
4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.264 |
|
| 12898 |
\begin{align*}
y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| 12899 |
\begin{align*}
y^{\prime }&=y^{p} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| 12900 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.265 |
|