| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 21001 |
\begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.725 |
|
| 21002 |
\begin{align*}
{y^{\prime \prime }}^{2}&={y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.725 |
|
| 21003 |
\begin{align*}
t^{2} y^{\prime }&=y^{2}+t y+t^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.727 |
|
| 21004 |
\begin{align*}
y^{\prime } x&=y^{2} x^{2}-y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.728 |
|
| 21005 |
\begin{align*}
y x^{\prime }+2 x&=5 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.732 |
|
| 21006 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.737 |
|
| 21007 |
\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*} |
✓ |
✓ |
✓ |
✓ |
6.737 |
|
| 21008 |
\begin{align*}
y^{\prime }&=y^{2}+a \cos \left (\beta x \right ) y+a b \cos \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.737 |
|
| 21009 |
\begin{align*}
\left (1+y+y x +y^{2}\right ) y^{\prime }+1+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.738 |
|
| 21010 |
\begin{align*}
t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.738 |
|
| 21011 |
\begin{align*}
6 y x -3 y^{2}+2 y+2 \left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.740 |
|
| 21012 |
\begin{align*}
5 y^{\prime \prime }+\frac {3 y^{\prime }}{x -3}+\frac {3 y}{\left (x -3\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.741 |
|
| 21013 |
\begin{align*}
5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.745 |
|
| 21014 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.747 |
|
| 21015 |
\begin{align*}
y^{\prime } x&=f \left (x \right ) y^{2}+n y+a \,x^{2 n} f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.748 |
|
| 21016 |
\begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.749 |
|
| 21017 |
\begin{align*}
x \left (a +y\right ) y^{\prime }&=y \left (B x +A \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.753 |
|
| 21018 |
\begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.755 |
|
| 21019 |
\begin{align*}
y^{\prime } x +a +x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.757 |
|
| 21020 |
\begin{align*}
t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.763 |
|
| 21021 |
\begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.766 |
|
| 21022 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.766 |
|
| 21023 |
\begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.767 |
|
| 21024 |
\begin{align*}
y^{\prime }+3 \cot \left (x \right ) y&=6 \cos \left (x \right ) y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.769 |
|
| 21025 |
\begin{align*}
x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.771 |
|
| 21026 |
\begin{align*}
y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.774 |
|
| 21027 |
\begin{align*}
2 x y^{2}-y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.775 |
|
| 21028 |
\begin{align*}
y^{\prime } x -2 x^{4}-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.778 |
|
| 21029 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
6.778 |
|
| 21030 |
\begin{align*}
2 y^{\prime } x&=y \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.779 |
|
| 21031 |
\begin{align*}
\left (a +x \right )^{2} y^{\prime }&=2 \left (a +x \right ) \left (b +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.779 |
|
| 21032 |
\begin{align*}
\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.779 |
|
| 21033 |
\begin{align*}
a \csc \left (x \right )^{2} y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.779 |
|
| 21034 |
\begin{align*}
y y^{\prime } x&=3 x^{6}+6 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.780 |
|
| 21035 |
\begin{align*}
y-\left (x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.783 |
|
| 21036 |
\begin{align*}
\left (1+t \right ) x^{\prime }+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.784 |
|
| 21037 |
\begin{align*}
-y^{\prime } x +y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.785 |
|
| 21038 |
\begin{align*}
y^{\prime }&=\left (4 x +y+2\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.786 |
|
| 21039 |
\begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.786 |
|
| 21040 |
\begin{align*}
-y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.787 |
|
| 21041 |
\begin{align*}
x^{\prime }&=\frac {t^{2}+x^{2}}{2 t x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.787 |
|
| 21042 |
\begin{align*}
x \left (y x +2\right ) y^{\prime }&=3+2 x^{3}-2 y-x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.788 |
|
| 21043 |
\begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.789 |
|
| 21044 |
\begin{align*}
-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {y^{\prime \prime }}{y}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y}&=2 a^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.792 |
|
| 21045 |
\begin{align*}
x^{2}+2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.792 |
|
| 21046 |
\begin{align*}
\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.796 |
|
| 21047 |
\begin{align*}
y^{\prime }&=a +b \sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.797 |
|
| 21048 |
\begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.798 |
|
| 21049 |
\begin{align*}
y^{\prime } x +2 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.802 |
|
| 21050 |
\begin{align*}
y^{\prime }&=\left (9 x -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.802 |
|
| 21051 |
\begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.802 |
|
| 21052 |
\begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.802 |
|
| 21053 |
\begin{align*}
x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| 21054 |
\begin{align*}
\frac {y^{\prime }}{2}&=\sqrt {1+y}\, \cos \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.807 |
|
| 21055 |
\begin{align*}
x^{\prime }&=\frac {x}{t}+\frac {x^{2}}{t^{3}} \\
x \left (2\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.809 |
|
| 21056 |
\begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.811 |
|
| 21057 |
\begin{align*}
y^{\prime }&=25+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.813 |
|
| 21058 |
\begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.816 |
|
| 21059 |
\begin{align*}
x^{2} \left (a +x \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b x +c \right ) y+x \alpha +\beta &=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.816 |
|
| 21060 |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.833 |
|
| 21061 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y&=0 \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
6.833 |
|
| 21062 |
\begin{align*}
3 y^{\prime } x +5 y&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.833 |
|
| 21063 |
\begin{align*}
x^{\prime \prime }+36 x&=0 \\
x \left (0\right ) &= 5 \\
x \left (\frac {\pi }{12}\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.837 |
|
| 21064 |
\begin{align*}
\left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.839 |
|
| 21065 |
\begin{align*}
x^{\prime \prime }&=x^{3}-x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
6.839 |
|
| 21066 |
\begin{align*}
y^{\prime }&=a y-b y^{2} \\
y \left (0\right ) &= \operatorname {y0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.842 |
|
| 21067 |
\begin{align*}
t^{2} y+t^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.842 |
|
| 21068 |
\begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.848 |
|
| 21069 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.851 |
|
| 21070 |
\begin{align*}
y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.852 |
|
| 21071 |
\begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.854 |
|
| 21072 |
\begin{align*}
y^{\prime } x&=5 y+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.860 |
|
| 21073 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.861 |
|
| 21074 |
\begin{align*}
y^{\prime }&=\frac {2 y}{t}+\frac {y^{2}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.862 |
|
| 21075 |
\begin{align*}
y^{\prime }&=f \left (x \right )+a y+b z \\
z^{\prime }&=g \left (x \right )+c y+d z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.862 |
|
| 21076 |
\begin{align*}
y^{\prime }-a y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.862 |
|
| 21077 |
\begin{align*}
\left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.871 |
|
| 21078 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.875 |
|
| 21079 |
\begin{align*}
y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.878 |
|
| 21080 |
\begin{align*}
\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.878 |
|
| 21081 |
\begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.879 |
|
| 21082 |
\begin{align*}
3 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.879 |
|
| 21083 |
\begin{align*}
y&=\left (2 x +1\right ) \left (1-y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.884 |
|
| 21084 |
\begin{align*}
-a y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.885 |
|
| 21085 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=a^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.885 |
|
| 21086 |
\begin{align*}
y^{\prime } x +2 y&=6 \sqrt {y}\, x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.888 |
|
| 21087 |
\begin{align*}
y+x^{3} y^{3}+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.888 |
|
| 21088 |
\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*} |
✓ |
✓ |
✓ |
✗ |
6.889 |
|
| 21089 |
\begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.894 |
|
| 21090 |
\begin{align*}
x^{2}-2 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.900 |
|
| 21091 |
\begin{align*}
y^{\prime }+\frac {x y}{a^{2}+x^{2}}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.901 |
|
| 21092 |
\begin{align*}
y^{\prime }+y x&=\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.901 |
|
| 21093 |
\begin{align*}
y^{\prime }&=\frac {y}{2 y \ln \left (y\right )+y-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.906 |
|
| 21094 |
\begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.911 |
|
| 21095 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.911 |
|
| 21096 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=-1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.914 |
|
| 21097 |
\begin{align*}
-2 \left (\cos \left (x \right )+1\right ) \sec \left (x \right ) y-\left (2+3 \cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.917 |
|
| 21098 |
\begin{align*}
y^{\prime }&=y^{2}-t \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.921 |
|
| 21099 |
\begin{align*}
\left (a +x \right ) y^{\prime }&=b x +c y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.923 |
|
| 21100 |
\begin{align*}
2 x \left (1+\sqrt {x^{2}-y}\right )&=\sqrt {x^{2}-y}\, y^{\prime } \\
\end{align*} |
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6.923 |
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