| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19801 |
\begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.174 |
|
| 19802 |
\begin{align*}
x^{\prime \prime }+x-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.175 |
|
| 19803 |
\begin{align*}
\left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.189 |
|
| 19804 |
\begin{align*}
y^{3} y^{\prime \prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.191 |
|
| 19805 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.191 |
|
| 19806 |
\begin{align*}
a \tan \left (\frac {x}{2}\right )^{2} y-\csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
8.194 |
|
| 19807 |
\begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.197 |
|
| 19808 |
\begin{align*}
3 x^{2} y^{3}-y^{2}+y+\left (-y x +2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.201 |
|
| 19809 |
\begin{align*}
y^{\prime }&=\frac {y+{\mathrm e}^{-\frac {y}{x}} x}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.202 |
|
| 19810 |
\begin{align*}
4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.202 |
|
| 19811 |
\begin{align*}
y^{\prime } x +2 y&=\frac {1}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.204 |
|
| 19812 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 y^{2} x^{4}+3 y x^{5}+x^{6}}{x \left (x^{2}+y x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.204 |
|
| 19813 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \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. |
✓ |
✓ |
✓ |
✓ |
8.206 |
|
| 19814 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.206 |
|
| 19815 |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.212 |
|
| 19816 |
\begin{align*}
6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.213 |
|
| 19817 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.217 |
|
| 19818 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.218 |
|
| 19819 |
\begin{align*}
y^{\prime }&={\mathrm e}^{t -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.221 |
|
| 19820 |
\begin{align*}
y^{\prime }&=\frac {x +y+3}{3 x +3 y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.221 |
|
| 19821 |
\begin{align*}
x^{4} {y^{\prime }}^{2}+2 y y^{\prime } x^{3}-4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.221 |
|
| 19822 |
\begin{align*}
y^{\prime }+\frac {x y}{-x^{2}+1}&=x \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.222 |
|
| 19823 |
\begin{align*}
y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.224 |
|
| 19824 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.225 |
|
| 19825 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.231 |
|
| 19826 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\
x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.231 |
|
| 19827 |
\begin{align*}
y^{\prime }&=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.234 |
|
| 19828 |
\begin{align*}
x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\
x \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.235 |
|
| 19829 |
\begin{align*}
2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.237 |
|
| 19830 |
\begin{align*}
y^{\prime } x +y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.238 |
|
| 19831 |
\begin{align*}
r^{\prime }+r \tan \left (t \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.239 |
|
| 19832 |
\begin{align*}
y^{\prime } x&=2 y+{\mathrm e}^{x} x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.240 |
|
| 19833 |
\begin{align*}
x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }&=6 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.241 |
|
| 19834 |
\begin{align*}
x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u&=0 \\
u \left (1\right ) &= -1 \\
u^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.244 |
|
| 19835 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.245 |
|
| 19836 |
\begin{align*}
y^{\prime }&=\frac {1+x^{2}+y^{2}}{2 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.245 |
|
| 19837 |
\begin{align*}
y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.250 |
|
| 19838 |
\begin{align*}
y^{\prime }&=\frac {t}{y+t^{2} y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.250 |
|
| 19839 |
\begin{align*}
x^{2} y^{\prime }+3 y x&=6 \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.250 |
|
| 19840 |
\begin{align*}
-x^{2} y-\left (-x^{3}+1\right ) y^{\prime }+x \left (x^{3}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.251 |
|
| 19841 |
\begin{align*}
y^{\prime }&=y^{2}+f \left (x \right ) y-a^{2}-a f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.253 |
|
| 19842 |
\begin{align*}
x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.257 |
|
| 19843 |
\begin{align*}
x^{4} y^{\prime }+2 x^{3} y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.258 |
|
| 19844 |
\begin{align*}
y^{2} \left (x^{2}+1\right )+y+\left (2 y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.263 |
|
| 19845 |
\begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.263 |
|
| 19846 |
\begin{align*}
y^{\prime }&=a x +b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.266 |
|
| 19847 |
\begin{align*}
y&=y^{\prime } x +\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.266 |
|
| 19848 |
\begin{align*}
2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.270 |
|
| 19849 |
\begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.273 |
|
| 19850 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.276 |
|
| 19851 |
\begin{align*}
y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.280 |
|
| 19852 |
\begin{align*}
y^{\prime \prime }-a y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.284 |
|
| 19853 |
\begin{align*}
3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.287 |
|
| 19854 |
\begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.289 |
|
| 19855 |
\begin{align*}
y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.292 |
|
| 19856 |
\begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.296 |
|
| 19857 |
\begin{align*}
c y^{\prime }&=a x +b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.301 |
|
| 19858 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.301 |
|
| 19859 |
\begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
8.302 |
|
| 19860 |
\begin{align*}
t x^{\prime \prime }&=x \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
8.302 |
|
| 19861 |
\begin{align*}
2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.307 |
|
| 19862 |
\begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.308 |
|
| 19863 |
\begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.312 |
|
| 19864 |
\begin{align*}
y^{\prime }&=-\frac {3 x^{2}+2 y^{2}}{4 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.313 |
|
| 19865 |
\begin{align*}
3 y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.319 |
|
| 19866 |
\begin{align*}
t^{2} y^{\prime \prime }-3 y^{\prime } t +5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.322 |
|
| 19867 |
\begin{align*}
y^{\prime } x&=y+x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.323 |
|
| 19868 |
\begin{align*}
y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.325 |
|
| 19869 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.325 |
|
| 19870 |
\begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.325 |
|
| 19871 |
\begin{align*}
3 \left (1-y\right ) y y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.330 |
|
| 19872 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.330 |
|
| 19873 |
\begin{align*}
\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.334 |
|
| 19874 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.338 |
|
| 19875 |
\begin{align*}
a {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.339 |
|
| 19876 |
\begin{align*}
y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\
y \left (-2\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.339 |
|
| 19877 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.342 |
|
| 19878 |
\begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.344 |
|
| 19879 |
\begin{align*}
y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.345 |
|
| 19880 |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (b \,x^{2}+a \left (x^{4}+1\right )\right ) y}{x^{4}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.345 |
|
| 19881 |
\begin{align*}
y^{\prime }&=y \cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.346 |
|
| 19882 |
\begin{align*}
\left (2 x -y^{2}\right ) y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.347 |
|
| 19883 |
\begin{align*}
1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.348 |
|
| 19884 |
\begin{align*}
\cos \left (x \right ) y^{\prime }-2 \sin \left (x \right ) y+3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.352 |
|
| 19885 |
\begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.354 |
|
| 19886 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=9 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.354 |
|
| 19887 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.355 |
|
| 19888 |
\begin{align*}
y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.358 |
|
| 19889 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.358 |
|
| 19890 |
\begin{align*}
x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.361 |
|
| 19891 |
\begin{align*}
\frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| 19892 |
\begin{align*}
y^{\prime }&=-{\mathrm e}^{-t^{2}} y+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| 19893 |
\begin{align*}
3 y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+4 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| 19894 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime }-x^{2}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.364 |
|
| 19895 |
\begin{align*}
x^{\prime \prime }&=\left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.365 |
|
| 19896 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.369 |
|
| 19897 |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+b \,x^{4}+b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+a \,x^{2} y^{2}+a x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.374 |
|
| 19898 |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
8.374 |
|
| 19899 |
\begin{align*}
y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.374 |
|
| 19900 |
\begin{align*}
x^{\prime }&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.375 |
|