| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25001 |
\begin{align*}
y^{\prime } y-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
43.417 |
|
| 25002 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
43.493 |
|
| 25003 |
\begin{align*}
y^{\prime }+\frac {\tan \left (y\right )}{x}&=\frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.510 |
|
| 25004 |
\begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.588 |
|
| 25005 |
\begin{align*}
2 y^{\prime }+a x&=-\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.662 |
|
| 25006 |
\begin{align*}
y^{2} y^{\prime } x +y^{3}&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.698 |
|
| 25007 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
43.739 |
|
| 25008 |
\begin{align*}
y y^{\prime \prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.781 |
|
| 25009 |
\begin{align*}
y^{\prime }&=1+x +x^{2} \cos \left (x \right )-\left (1+4 \cos \left (x \right ) x \right ) y+2 y^{2} \cos \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
43.947 |
|
| 25010 |
\begin{align*}
x^{\prime }&=n y-m z \\
y^{\prime }&=L z-m x \\
z^{\prime }&=m x-L y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.079 |
|
| 25011 |
\begin{align*}
{y^{\prime }}^{3}-y^{\prime } x +a y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
44.204 |
|
| 25012 |
\begin{align*}
\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime }&={\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.345 |
|
| 25013 |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=\frac {6+x}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
44.346 |
|
| 25014 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2}-1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
44.348 |
|
| 25015 |
\begin{align*}
a \sin \left (y\right )+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.401 |
|
| 25016 |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y-1\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right )^{2} x \left (1+y\right )^{2}}{16} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
44.473 |
|
| 25017 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
44.487 |
|
| 25018 | \begin{align*}
2 y^{\prime }+a x&=\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 44.829 |
|
| 25019 |
\begin{align*}
3 x -y-5+\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.882 |
|
| 25020 |
\begin{align*}
y^{\prime }&=a \,x^{m}+b \,x^{n} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.997 |
|
| 25021 |
\begin{align*}
x \left (x +y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.013 |
|
| 25022 |
\begin{align*}
y^{\prime } x +y&=y^{2} x^{3} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.030 |
|
| 25023 |
\begin{align*}
y^{2}+\left (x^{2}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.086 |
|
| 25024 |
\begin{align*}
y^{\prime } x&=\sqrt {y^{2}+x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.141 |
|
| 25025 |
\begin{align*}
y^{\prime }&=\frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.248 |
|
| 25026 |
\begin{align*}
y^{\prime } x&=f \left (x \right ) \left (y+a \ln \left (x \right )\right )^{2}-a \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
45.381 |
|
| 25027 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
45.410 |
|
| 25028 |
\begin{align*}
x^{3}-y^{3}+y^{2} y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.417 |
|
| 25029 |
\begin{align*}
\left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime }&=-x^{2} \sqrt {x^{2}-y^{2}}+y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
45.447 |
|
| 25030 |
\begin{align*}
y^{\prime }-\frac {1+y}{x +1}&=\sqrt {1+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.606 |
|
| 25031 |
\begin{align*}
y^{\prime }&=a \cos \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.682 |
|
| 25032 |
\begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.764 |
|
| 25033 |
\begin{align*}
\sin \left (x \right )+\cos \left (y\right )+\cos \left (x \right )-y^{\prime } \sin \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.778 |
|
| 25034 |
\begin{align*}
9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
45.819 |
|
| 25035 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) \left (-y+y^{\prime } x \right )+s \,x^{k} \left (y^{2}-\lambda \,x^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.987 |
|
| 25036 |
\begin{align*}
y^{\prime }&=\lambda \cos \left (\lambda x \right ) y^{2}+\lambda \cos \left (\lambda x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
46.104 |
|
| 25037 | \begin{align*}
\left (y^{\prime } x +y\right )^{2}&=y^{2} y^{\prime } \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 46.163 |
|
| 25038 |
\begin{align*}
y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
46.246 |
|
| 25039 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=1+y+\left (x +1\right ) \sqrt {1+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
46.320 |
|
| 25040 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 a -3\right ) x y^{\prime }+\left (n +1\right ) \left (n +2 a -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
46.349 |
|
| 25041 |
\begin{align*}
y^{\prime }&=\left (a \cosh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
46.502 |
|
| 25042 |
\begin{align*}
y^{\prime }-a \sqrt {1+y^{2}}-b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
46.625 |
|
| 25043 |
\begin{align*}
y^{\prime } y-\frac {a \left (5 x -4\right ) y}{x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
46.646 |
|
| 25044 |
\begin{align*}
y^{\prime } y&=\left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
46.733 |
|
| 25045 |
\begin{align*}
g \left (x \right ) y^{\prime }+f \left (x \right ) {y^{\prime }}^{k}+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
46.787 |
|
| 25046 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+h \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
46.809 |
|
| 25047 |
\begin{align*}
y^{\prime } y-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
46.848 |
|
| 25048 |
\begin{align*}
x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (x^{4} y^{2}-1\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
46.853 |
|
| 25049 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
46.905 |
|
| 25050 |
\begin{align*}
p \left (2 k +p \right ) y-\left (1+2 k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
46.922 |
|
| 25051 |
\begin{align*}
3 x^{2}-2 y x +\left (4 y^{3}-x^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
46.958 |
|
| 25052 |
\begin{align*}
y^{2} y^{\prime } x +y^{3}&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
47.005 |
|
| 25053 |
\begin{align*}
\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
47.071 |
|
| 25054 |
\begin{align*}
\left (-y+y^{\prime } x \right ) \left (x -y^{\prime } y\right )&=2 y^{\prime } \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
47.078 |
|
| 25055 |
\begin{align*}
y^{\prime }&=-f^{\prime }\left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y-g \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
47.124 |
|
| 25056 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \arccos \left (x \right )^{n} y+\arccos \left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
47.253 |
|
| 25057 | \begin{align*}
y^{\prime }&=-\frac {x^{2} \left (a x -2 \sqrt {a \left (a \,x^{4}+8 y\right )}\right )}{2} \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 47.339 |
|
| 25058 |
\begin{align*}
x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
47.353 |
|
| 25059 |
\begin{align*}
y^{\prime } y&=\left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
47.377 |
|
| 25060 |
\begin{align*}
-4 x -y-1+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
47.464 |
|
| 25061 |
\begin{align*}
y^{\prime \prime }-x^{3} y-x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
47.465 |
|
| 25062 |
\begin{align*}
2 y^{\prime \prime }&=\sin \left (2 y\right ) \\
y \left (0\right ) &= -\frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
47.704 |
|
| 25063 |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
47.706 |
|
| 25064 |
\begin{align*}
y^{\prime }&=\frac {c t -a y}{A t +b y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
47.760 |
|
| 25065 |
\begin{align*}
x^{\prime \prime }-x^{\prime }+x-x^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
47.795 |
|
| 25066 |
\begin{align*}
x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y^{\prime } y-2 y x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
47.849 |
|
| 25067 |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arcsin \left (x \right )^{n} y+b m \,x^{m -1} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
47.924 |
|
| 25068 |
\begin{align*}
\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
47.945 |
|
| 25069 |
\begin{align*}
16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
47.966 |
|
| 25070 |
\begin{align*}
y^{\prime }&=\frac {y \left (x -y\right ) \left (1+y\right )}{x \left (y x +x -y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.167 |
|
| 25071 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \tan \left (x \right )^{m} y-a \tan \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.358 |
|
| 25072 |
\begin{align*}
y^{\prime }&=\frac {y \left (x +y\right ) \left (1+y\right )}{x \left (y x +x +y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.372 |
|
| 25073 |
\begin{align*}
y^{\prime }&=-\frac {\left (-\ln \left (y-1\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
48.492 |
|
| 25074 |
\begin{align*}
x -1-\left (3 x -2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.529 |
|
| 25075 |
\begin{align*}
L x^{\prime \prime }+g \sin \left (x\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.559 |
|
| 25076 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
48.577 |
|
| 25077 | \begin{align*}
\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 48.697 |
|
| 25078 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
48.875 |
|
| 25079 |
\begin{align*}
\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.892 |
|
| 25080 |
\begin{align*}
y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
48.963 |
|
| 25081 |
\begin{align*}
x^{3}+y^{3}+y^{2} \left (3 x +k y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.009 |
|
| 25082 |
\begin{align*}
y^{\prime }-\frac {1+y^{2}}{{| y+\sqrt {1+y}|} \left (x +1\right )^{{3}/{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.078 |
|
| 25083 |
\begin{align*}
x^{\prime \prime }+\sin \left (x\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.154 |
|
| 25084 |
\begin{align*}
y+2 \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.174 |
|
| 25085 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \arcsin \left (x \right )^{n} y+\arcsin \left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.269 |
|
| 25086 |
\begin{align*}
y^{\prime } y-y&=\frac {A}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.303 |
|
| 25087 |
\begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
49.493 |
|
| 25088 |
\begin{align*}
\frac {y^{\prime } y+x}{\sqrt {y^{2}+x^{2}}}&=m \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.501 |
|
| 25089 |
\begin{align*}
x^{2}-y x +y^{2}-x y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.556 |
|
| 25090 |
\begin{align*}
\left (x^{2}+2 y x \right ) y^{\prime }-3 x^{2}+2 y x -y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.566 |
|
| 25091 |
\begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= -{\frac {1}{4}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
49.572 |
|
| 25092 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-4 x+4 y-2 z \\
z^{\prime }&=-4 y+4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.599 |
|
| 25093 |
\begin{align*}
y^{\prime }&=\frac {x}{y+\sqrt {x^{2}+1}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.791 |
|
| 25094 |
\begin{align*}
m y^{\prime \prime }+k \sin \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.859 |
|
| 25095 |
\begin{align*}
z^{\prime \prime }+z+z^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.891 |
|
| 25096 | \begin{align*}
\left (2 y x +2 x^{2}\right ) y^{\prime }&=x^{2}+2 y x +2 y^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 49.898 |
|
| 25097 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (\nu +n +1\right ) \left (\nu -n \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.102 |
|
| 25098 |
\begin{align*}
y^{\prime } x -y+y^{2}&=x^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.119 |
|
| 25099 |
\begin{align*}
y^{\prime }&=\frac {x^{3} {\mathrm e}^{y}+x^{4}+{\mathrm e}^{y} y-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+y x -\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.217 |
|
| 25100 |
\begin{align*}
y^{\prime }+x^{-a -1} y^{2}-x^{a}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.410 |
|