| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 27201 |
\begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
86.372 |
|
| 27202 |
\begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (4\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
86.464 |
|
| 27203 |
\begin{align*}
-2 y x +\left (3 x^{2}-2 y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
86.477 |
|
| 27204 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+\lambda a \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
86.537 |
|
| 27205 |
\begin{align*}
\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
86.715 |
|
| 27206 |
\begin{align*}
x \left (3-y x \right ) y^{\prime }&=y \left (y x -1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
87.181 |
|
| 27207 |
\begin{align*}
y y^{\prime \prime }&=-b y^{2}-a y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
87.310 |
|
| 27208 |
\begin{align*}
y y^{\prime }-y&=a x +b \,x^{m} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
87.310 |
|
| 27209 |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
87.341 |
|
| 27210 |
\begin{align*}
b y+a \left (y^{2}-1\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
87.363 |
|
| 27211 |
\begin{align*}
x^{2} \left (x -2 y\right ) y^{\prime }&=2 x^{3}-4 x y^{2}+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
87.370 |
|
| 27212 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
87.442 |
|
| 27213 |
\begin{align*}
y y^{\prime }-y&=a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
87.598 |
|
| 27214 |
\begin{align*}
y y^{\prime }-y&=20 x +\frac {A}{\sqrt {x}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
87.689 |
|
| 27215 |
\begin{align*}
\left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
87.811 |
|
| 27216 |
\begin{align*}
x^{2} y^{\prime }&=a +b \,x^{n}+c \,x^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
87.852 |
|
| 27217 |
\begin{align*}
\left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (x +1\right ) \eta ^{\prime }+\left (1+k \right ) \eta &=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
88.290 |
|
| 27218 |
\begin{align*}
3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
88.581 |
|
| 27219 |
\begin{align*}
y^{\prime }&=x \left (y-4\right )^{2}-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
88.670 |
|
| 27220 |
\begin{align*}
\left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.131 |
|
| 27221 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+\lambda a \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
89.300 |
|
| 27222 |
\begin{align*}
\left (a \,x^{2}+2 y x -a y^{2}\right ) y^{\prime }+x^{2}-2 a x y-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
89.385 |
|
| 27223 |
\begin{align*}
\frac {x}{\sqrt {\left (x^{2}+y^{2}\right ) \left (1-x^{2}-y^{2}\right )}}+\frac {y y^{\prime }}{\sqrt {\left (x^{2}+y^{2}\right ) \left (1-x^{2}-y^{2}\right )}}+\left (\frac {1}{y \sqrt {y^{2}-x^{2}}}+\frac {{\mathrm e}^{\frac {x}{y}}}{y^{2}}\right ) y-x \left (\frac {1}{y \sqrt {y^{2}-x^{2}}}+\frac {{\mathrm e}^{\frac {x}{y}}}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
89.399 |
|
| 27224 |
\begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
89.436 |
|
| 27225 |
\begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.704 |
|
| 27226 |
\begin{align*}
\left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
89.759 |
|
| 27227 |
\begin{align*}
y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
89.800 |
|
| 27228 |
\begin{align*}
\left (a \cosh \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \cosh \left (\mu x \right ) y-d^{2}+c d \cosh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.907 |
|
| 27229 |
\begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.987 |
|
| 27230 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
90.014 |
|
| 27231 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
90.015 |
|
| 27232 |
\begin{align*}
{y^{\prime }}^{2} x +2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
90.088 |
|
| 27233 |
\begin{align*}
x \left (2 x^{3}+y\right ) y^{\prime }&=\left (2 x^{3}-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
90.189 |
|
| 27234 |
\begin{align*}
-a^{2} y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
90.217 |
|
| 27235 |
\begin{align*}
x y^{\prime }&=a \tan \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \tan \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
90.255 |
|
| 27236 |
\begin{align*}
\left (x^{2}+y^{2}\right ) \left (y^{\prime }+1\right )^{2}-2 \left (x +y\right ) \left (y^{\prime }+1\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
90.435 |
|
| 27237 |
\begin{align*}
{\mathrm e}^{x} \cos \left (y\right )-x^{2}+\left ({\mathrm e}^{y} \sin \left (x \right )+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
90.727 |
|
| 27238 |
\begin{align*}
y y^{\prime }-\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*} |
✗ |
✓ |
✗ |
✗ |
90.870 |
|
| 27239 |
\begin{align*}
y y^{\prime }&=1-x {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
90.918 |
|
| 27240 |
\begin{align*}
\left (-x^{2}+1\right ) z^{\prime \prime }+\left (-3 x +1\right ) z^{\prime }+k z&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
90.939 |
|
| 27241 |
\begin{align*}
y^{2}&=\left (x^{2}+2 y x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
91.246 |
|
| 27242 |
\begin{align*}
\frac {1}{{y^{\prime }}^{2}}+x y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
91.718 |
|
| 27243 |
\begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
91.757 |
|
| 27244 |
\begin{align*}
{\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
91.768 |
|
| 27245 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
91.779 |
|
| 27246 |
\begin{align*}
2 x^{2} y^{\prime }&=2 y x +\left (-x \cot \left (x \right )+1\right ) \left (x^{2}-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
91.787 |
|
| 27247 |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
91.795 |
|
| 27248 |
\begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
91.812 |
|
| 27249 |
\begin{align*}
y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
91.937 |
|
| 27250 |
\begin{align*}
\left (c^{2} x^{2}+b^{2}\right ) y-x y^{\prime }+\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
92.048 |
|
| 27251 |
\begin{align*}
y^{\prime }&=\frac {y}{x -k \sqrt {x^{2}+y^{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
92.337 |
|
| 27252 |
\begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }+x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
92.369 |
|
| 27253 |
\begin{align*}
y&=2 x +y^{\prime }-\frac {{y^{\prime }}^{3}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
92.661 |
|
| 27254 |
\begin{align*}
x y^{\prime }&=a \cot \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cot \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
92.992 |
|
| 27255 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-x y^{\prime }+y \,{\mathrm e}^{x}&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
93.184 |
|
| 27256 |
\begin{align*}
-x^{\prime \prime }&=1-x-x^{2} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
93.271 |
|
| 27257 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+t^{2} y&=\cos \left (t \right ) \\
y \left (0\right ) &= y_{1} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
93.398 |
|
| 27258 |
\begin{align*}
\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
93.477 |
|
| 27259 |
\begin{align*}
\left (-x^{2}+1\right )^{2} y^{\prime \prime }-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (\nu \left (\nu +1\right ) \left (-x^{2}+1\right )-\mu ^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
93.520 |
|
| 27260 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
93.716 |
|
| 27261 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
93.786 |
|
| 27262 |
\begin{align*}
\left (\sinh \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
93.860 |
|
| 27263 |
\begin{align*}
y^{2}+\left (t^{2}+y t \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
93.879 |
|
| 27264 |
\begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
93.951 |
|
| 27265 |
\begin{align*}
x -\frac {y}{y^{\prime }}&=\frac {2}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
94.040 |
|
| 27266 |
\begin{align*}
x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\
y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\
z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
94.423 |
|
| 27267 |
\begin{align*}
y&={y^{\prime }}^{2} x -\frac {1}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
94.456 |
|
| 27268 |
\begin{align*}
8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
94.512 |
|
| 27269 |
\begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a^{2} \left (n +1\right ) x^{2 n}+n -1\right ) y^{\prime }-\nu \left (\nu +1\right ) a^{2} n^{2} x^{2 n} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
94.691 |
|
| 27270 |
\begin{align*}
\left (b x +a \right ) y+\left (1-2 x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
95.039 |
|
| 27271 |
\begin{align*}
\left (2 A x y+B \,x^{2}+b \right ) y^{\prime }&=A y^{2}+k \left (A k +B \right ) x^{2}+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
95.062 |
|
| 27272 |
\begin{align*}
y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
95.135 |
|
| 27273 |
\begin{align*}
\frac {1}{x^{2}-y x +y^{2}}&=\frac {y^{\prime }}{2 y^{2}-y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
95.180 |
|
| 27274 |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
95.444 |
|
| 27275 |
\begin{align*}
\left (A y+B x +a \right ) y^{\prime }+B y+k x +b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
95.445 |
|
| 27276 |
\begin{align*}
y^{2}+\left (3 y x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
95.566 |
|
| 27277 |
\begin{align*}
\left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
95.595 |
|
| 27278 |
\begin{align*}
y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y&=-a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
95.601 |
|
| 27279 |
\begin{align*}
{y^{\prime }}^{3}-2 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
95.624 |
|
| 27280 |
\begin{align*}
x^{\prime \prime }&=x^{2}-4 x+\lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
95.723 |
|
| 27281 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=a \,x^{-2+n} y^{2}+b \,x^{m -1} y+c \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
95.883 |
|
| 27282 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 x}+\left (2+\frac {5 \,{\mathrm e}^{x}}{2}\right ) y+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
95.954 |
|
| 27283 |
\begin{align*}
\operatorname {A2} \left (a x +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (a x +b \right ) y^{\prime }+\operatorname {A0} \left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
96.189 |
|
| 27284 |
\begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
96.226 |
|
| 27285 |
\begin{align*}
\left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (a -x^{2}+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
96.299 |
|
| 27286 |
\begin{align*}
\left (a_{2} +b_{2} x +c_{2} y\right ) y^{\prime }&=a_{1} +b_{1} x +c_{1} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
96.440 |
|
| 27287 |
\begin{align*}
x \left (y+x^{3}\right ) y^{\prime }&=\left (x^{3}-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
96.493 |
|
| 27288 |
\begin{align*}
x^{4}+y^{4}-x y^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
96.533 |
|
| 27289 |
\begin{align*}
x y^{\prime }&=x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
96.599 |
|
| 27290 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{y x +\left (x y^{2}\right )^{{1}/{3}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
96.681 |
|
| 27291 |
\begin{align*}
2 y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
96.760 |
|
| 27292 |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
97.241 |
|
| 27293 |
\begin{align*}
{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
97.479 |
|
| 27294 |
\begin{align*}
\left (x -y\right ) \left (4 x +y\right )+x \left (5 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
97.486 |
|
| 27295 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }+\left (\left (x^{2}-1\right ) \left (a^{2} x^{2}-\lambda \right )-m^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
97.529 |
|
| 27296 |
\begin{align*}
x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
97.595 |
|
| 27297 |
\begin{align*}
3 y^{\prime }&=x -\sqrt {x^{2}-3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
97.709 |
|
| 27298 |
\begin{align*}
\left (a_{2} +b x +c_{2} y\right ) y^{\prime }+a_{1} +b_{1} x +b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
97.866 |
|
| 27299 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
97.901 |
|
| 27300 |
\begin{align*}
x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
97.989 |
|