| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 17801 |
\begin{align*}
-y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.983 |
|
| 17802 |
\begin{align*}
y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.984 |
|
| 17803 |
\begin{align*}
y^{\prime }&=-\frac {y}{t +1}+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.984 |
|
| 17804 |
\begin{align*}
2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.984 |
|
| 17805 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.985 |
|
| 17806 |
\begin{align*}
y^{\prime }&=\sqrt {4 x +2 y-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.986 |
|
| 17807 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.987 |
|
| 17808 |
\begin{align*}
\left (x +a \right ) y^{\prime }&=b x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.987 |
|
| 17809 |
\begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| 17810 |
\begin{align*}
y^{\prime \prime }&=\frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.988 |
|
| 17811 |
\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*} |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| 17812 |
\begin{align*}
\frac {y^{\prime }}{y}&=y-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| 17813 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x -y}}{1+{\mathrm e}^{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.989 |
|
| 17814 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{x +2}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.989 |
|
| 17815 |
\begin{align*}
x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.989 |
|
| 17816 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.990 |
|
| 17817 |
\begin{align*}
y^{\prime }&=\sqrt {y \left (1-y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.990 |
|
| 17818 |
\begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.990 |
|
| 17819 |
\begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| 17820 |
\begin{align*}
y^{\prime }&=-x \,{\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| 17821 |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+y \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| 17822 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+36 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| 17823 |
\begin{align*}
y^{\prime }&=x^{3} \left (1-y\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| 17824 |
\begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| 17825 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.995 |
|
| 17826 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.997 |
|
| 17827 |
\begin{align*}
y^{\prime }&=\frac {-2 x -y+1+x^{2} y^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.997 |
|
| 17828 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.997 |
|
| 17829 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +y}+x^{2} {\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.997 |
|
| 17830 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.997 |
|
| 17831 |
\begin{align*}
\frac {t y}{t^{2}+1}+y^{\prime }&=1-\frac {t^{3} y}{t^{4}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.999 |
|
| 17832 |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.000 |
|
| 17833 |
\begin{align*}
x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.001 |
|
| 17834 |
\begin{align*}
2 y y^{\prime }-x y^{2}-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.001 |
|
| 17835 |
\begin{align*}
y^{\prime }-y \,{\mathrm e}^{x}&=2 x \,{\mathrm e}^{{\mathrm e}^{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.001 |
|
| 17836 |
\begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.001 |
|
| 17837 |
\begin{align*}
2 y y^{\prime \prime }&=8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.002 |
|
| 17838 |
\begin{align*}
y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.003 |
|
| 17839 |
\begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| 17840 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| 17841 |
\begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| 17842 |
\begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (-4+t \right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (-4+t \right ) \\
y \left (0\right ) &= {\frac {3}{4}} \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| 17843 |
\begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| 17844 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.006 |
|
| 17845 |
\begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
3.006 |
|
| 17846 |
\begin{align*}
y^{\prime }&=y^{2}-y-6 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.006 |
|
| 17847 |
\begin{align*}
y^{\prime }&=\frac {3 x^{2}}{1+x^{3}+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.006 |
|
| 17848 |
\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. |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| 17849 |
\begin{align*}
y^{\prime }&=\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.007 |
|
| 17850 |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| 17851 |
\begin{align*}
y^{\prime }-\frac {3 y}{x -1}&=\left (x -1\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.008 |
|
| 17852 |
\begin{align*}
x^{2}+y&=x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| 17853 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\sin \left (x \right )}+\cos \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| 17854 |
\begin{align*}
y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}+\frac {y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.009 |
|
| 17855 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| 17856 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| 17857 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.011 |
|
| 17858 |
\begin{align*}
\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.011 |
|
| 17859 |
\begin{align*}
{y^{\prime }}^{2} x&=y-y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.012 |
|
| 17860 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| 17861 |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| 17862 |
\begin{align*}
a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| 17863 |
\begin{align*}
2 y a^{2} b^{2}+2 \left (a^{2}+b^{2}\right ) y^{\prime \prime }+2 y^{\prime \prime \prime \prime }&=\cos \left (a x \right )+\cos \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| 17864 |
\begin{align*}
y+y^{\prime }&=2-{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| 17865 |
\begin{align*}
\cot \left (y\right )-\tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| 17866 |
\begin{align*}
y^{\prime }&=2 x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| 17867 |
\begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.014 |
|
| 17868 |
\begin{align*}
t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y&=-\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.015 |
|
| 17869 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| 17870 |
\begin{align*}
t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| 17871 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\sin \left (x \right )}-\cos \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| 17872 |
\begin{align*}
{y^{\prime }}^{3}&=y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| 17873 |
\begin{align*}
y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| 17874 |
\begin{align*}
x y y^{\prime }-\left (x +1\right ) \sqrt {-1+y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.017 |
|
| 17875 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= \pi \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.017 |
|
| 17876 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= \alpha \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.017 |
|
| 17877 |
\begin{align*}
2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.017 |
|
| 17878 |
\begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.017 |
|
| 17879 |
\begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
3.018 |
|
| 17880 |
\begin{align*}
t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| 17881 |
\begin{align*}
-x y^{\prime }+y&=2 y^{\prime }+2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| 17882 |
\begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| 17883 |
\begin{align*}
y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| 17884 |
\begin{align*}
2 x \left (y+1\right )-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| 17885 |
\begin{align*}
y^{\prime }&=\sqrt {-x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| 17886 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.020 |
|
| 17887 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.020 |
|
| 17888 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.021 |
|
| 17889 |
\begin{align*}
-y+y^{\prime }&=\sin \left (\omega t \right )+\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.021 |
|
| 17890 |
\begin{align*}
\frac {1}{x}+\frac {y^{\prime }}{y}+\frac {2}{y}-\frac {2 y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| 17891 |
\begin{align*}
x y^{\prime }-y \left (\ln \left (y x \right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| 17892 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| 17893 |
\begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| 17894 |
\begin{align*}
y^{\prime }&=x \left (y^{2}-1\right )^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| 17895 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| 17896 |
\begin{align*}
1+y-\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.024 |
|
| 17897 |
\begin{align*}
z^{\prime }+7 y-9 z&={\mathrm e}^{x} \\
y^{\prime }-y-3 z&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.024 |
|
| 17898 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.025 |
|
| 17899 |
\begin{align*}
y y^{\prime \prime }&=-y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.025 |
|
| 17900 |
\begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.025 |
|