| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 24001 |
\begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.735 |
|
| 24002 |
\begin{align*}
y^{\prime }&=-\frac {i \left (32 i x +64+64 y^{4}+32 x^{2} y^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 y^{2} x^{4}+x^{6}\right )}{128 y} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
11.740 |
|
| 24003 |
\begin{align*}
y^{\prime }&=-\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.746 |
|
| 24004 |
\begin{align*}
{\mathrm e}^{x} y^{\prime }&=2 x y^{2}+y \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.753 |
|
| 24005 |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.763 |
|
| 24006 |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.769 |
|
| 24007 |
\begin{align*}
h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
11.769 |
|
| 24008 |
\begin{align*}
y^{\prime }&=\frac {1}{y x -3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.770 |
|
| 24009 |
\begin{align*}
x y^{\prime }+y&=x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.770 |
|
| 24010 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {2}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.772 |
|
| 24011 |
\begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.773 |
|
| 24012 |
\begin{align*}
y^{\prime }&=\frac {y^{2}-3 y x -5 x^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.773 |
|
| 24013 |
\begin{align*}
y^{\prime \prime \prime }&=y^{\prime } \left (y^{\prime }+1\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
11.774 |
|
| 24014 |
\begin{align*}
\left (\sinh \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \sinh \left (\lambda x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.774 |
|
| 24015 |
\begin{align*}
2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.775 |
|
| 24016 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.780 |
|
| 24017 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.782 |
|
| 24018 |
\begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.786 |
|
| 24019 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (3 x^{2}-4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.787 |
|
| 24020 |
\begin{align*}
y^{\prime } \sqrt {b^{2}-y^{2}}&=\sqrt {a^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.789 |
|
| 24021 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.790 |
|
| 24022 |
\begin{align*}
x y^{\prime }&=a \,x^{n +2} y^{3}+\left (b \,x^{n}-1\right ) y+c \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.792 |
|
| 24023 |
\begin{align*}
\left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.793 |
|
| 24024 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.793 |
|
| 24025 |
\begin{align*}
x y y^{\prime }+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.794 |
|
| 24026 |
\begin{align*}
2 y x -\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.796 |
|
| 24027 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.798 |
|
| 24028 |
\begin{align*}
y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.801 |
|
| 24029 |
\begin{align*}
x y^{\prime }+y&=x^{4} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.801 |
|
| 24030 |
\begin{align*}
y^{\prime }&=\frac {y}{\left (\ln \left (x \right )-\ln \left (y\right )\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.803 |
|
| 24031 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=4 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.805 |
|
| 24032 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.805 |
|
| 24033 |
\begin{align*}
y^{\prime }&=\frac {y \left (y-{\mathrm e}^{x}\right )}{{\mathrm e}^{x}-2 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.807 |
|
| 24034 |
\begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.810 |
|
| 24035 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.810 |
|
| 24036 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.822 |
|
| 24037 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\lambda x} y^{2}+c y-2 a \,b^{3} {\mathrm e}^{\lambda x}+b c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.823 |
|
| 24038 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.827 |
|
| 24039 |
\begin{align*}
y^{\prime }+2 y x&=-\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.829 |
|
| 24040 |
\begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.832 |
|
| 24041 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.834 |
|
| 24042 |
\begin{align*}
\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.835 |
|
| 24043 |
\begin{align*}
\left (x^{4}+y^{2}\right ) y^{\prime }&=4 x^{3} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.840 |
|
| 24044 |
\begin{align*}
y^{\prime }&=1-\left (x -y\right )^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.848 |
|
| 24045 |
\begin{align*}
y^{\prime }&=\frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.855 |
|
| 24046 |
\begin{align*}
x y^{\prime }&=y-x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.857 |
|
| 24047 |
\begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.858 |
|
| 24048 |
\begin{align*}
y^{\prime }&=\frac {y}{2 x}+\frac {x^{2}}{2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.863 |
|
| 24049 |
\begin{align*}
y^{\prime }-\frac {y}{t}&=t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.863 |
|
| 24050 |
\begin{align*}
\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.866 |
|
| 24051 |
\begin{align*}
y \left (2-3 y x \right )-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.868 |
|
| 24052 |
\begin{align*}
\left (2 x^{2}+1\right ) y y^{\prime }&=2 x \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.868 |
|
| 24053 |
\begin{align*}
y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.871 |
|
| 24054 |
\begin{align*}
x^{2} \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b \,x^{2}+c \right ) y+s&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.872 |
|
| 24055 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.882 |
|
| 24056 |
\begin{align*}
y^{\prime }&=\frac {y^{{3}/{2}} \left (x -y+\sqrt {y}\right )}{x y^{{3}/{2}}-y^{{5}/{2}}+y^{2}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.883 |
|
| 24057 |
\begin{align*}
y^{2} \left (x -1\right )&=x \left (y x +x -2 y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.883 |
|
| 24058 |
\begin{align*}
x y^{\prime }&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.890 |
|
| 24059 |
\begin{align*}
y^{\prime }&=\frac {3-2 x}{y} \\
y \left (1\right ) &= -6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.894 |
|
| 24060 |
\begin{align*}
y^{\prime }&=\frac {y x +3 x -2 y+6}{y x -3 x -2 y+6} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
11.898 |
|
| 24061 |
\begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.902 |
|
| 24062 |
\begin{align*}
n y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.905 |
|
| 24063 |
\begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.909 |
|
| 24064 |
\begin{align*}
2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.910 |
|
| 24065 |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
11.914 |
|
| 24066 |
\begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.917 |
|
| 24067 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=\frac {5}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.921 |
|
| 24068 |
\begin{align*}
2 x^{2} y^{\prime }&=y^{2} \left (2 x y^{\prime }-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.921 |
|
| 24069 |
\begin{align*}
x y^{\prime }+2&=x^{3} \left (-1+y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.924 |
|
| 24070 |
\begin{align*}
2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.932 |
|
| 24071 |
\begin{align*}
y^{\prime }&=\frac {y-\sqrt {x^{2}+y^{2}}}{x} \\
y \left (3\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.933 |
|
| 24072 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.935 |
|
| 24073 |
\begin{align*}
y^{\prime }&=\frac {1}{x -3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.938 |
|
| 24074 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \operatorname {arccot}\left (x \right )^{n} y+\operatorname {arccot}\left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.941 |
|
| 24075 |
\begin{align*}
y^{\prime }&=k \left (a -y\right ) \left (b -y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.942 |
|
| 24076 |
\begin{align*}
y y^{\prime }+x&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.949 |
|
| 24077 |
\begin{align*}
y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.951 |
|
| 24078 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.954 |
|
| 24079 |
\begin{align*}
x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y&=4 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.958 |
|
| 24080 |
\begin{align*}
y \sin \left (x \right )^{2}-\left (\cot \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.963 |
|
| 24081 |
\begin{align*}
y^{\prime }&=\left (a +b x y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.964 |
|
| 24082 |
\begin{align*}
\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.964 |
|
| 24083 |
\begin{align*}
x y^{\prime \prime }+\left (-x +b \right ) y^{\prime }-a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.976 |
|
| 24084 |
\begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.980 |
|
| 24085 |
\begin{align*}
{y^{\prime }}^{2}&=\left (-1+y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.982 |
|
| 24086 |
\begin{align*}
x y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.985 |
|
| 24087 |
\begin{align*}
x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.992 |
|
| 24088 |
\begin{align*}
4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.993 |
|
| 24089 |
\begin{align*}
y^{\prime }-\frac {y+1}{x +1}&=\sqrt {y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.006 |
|
| 24090 |
\begin{align*}
\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.008 |
|
| 24091 |
\begin{align*}
x^{2} y^{\prime \prime }+a y^{\prime }-y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
12.017 |
|
| 24092 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.026 |
|
| 24093 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
12.033 |
|
| 24094 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.042 |
|
| 24095 |
\begin{align*}
x y^{\prime }&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| 24096 |
\begin{align*}
y^{\prime }&=1+\frac {2 y}{x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| 24097 |
\begin{align*}
x^{2} y^{\prime }+y \left (x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| 24098 |
\begin{align*}
x^{2}+y^{2}+\left (2 y x -3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.047 |
|
| 24099 |
\begin{align*}
x^{2} y^{\prime }&=x^{2} y^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
12.049 |
|
| 24100 |
\begin{align*}
y^{3} y^{\prime }+x y^{4}&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.052 |
|