| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 24201 |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.375 |
|
| 24202 |
\begin{align*}
y^{\prime }+\frac {\left (2 x +1\right ) y}{x}&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.382 |
|
| 24203 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}&=y^{2} x^{2}+x^{4} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.423 |
|
| 24204 |
\begin{align*}
20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.464 |
|
| 24205 |
\begin{align*}
x \left (x^{2}-6 y^{2}\right ) y^{\prime }&=4 \left (x^{2}+3 y^{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.486 |
|
| 24206 |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.486 |
|
| 24207 |
\begin{align*}
\frac {y+\sin \left (x \right ) \cos \left (y x \right )^{2}}{\cos \left (y x \right )^{2}}+\left (\frac {x}{\cos \left (y x \right )^{2}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
18.510 |
|
| 24208 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {2}\, \sqrt {\frac {x +y}{x}}}{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.582 |
|
| 24209 |
\begin{align*}
x^{\prime }&=\tan \left (x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.639 |
|
| 24210 |
\begin{align*}
\left (a y-b x \right )^{2} \left (a^{2} {y^{\prime }}^{2}+b^{2}\right )-c^{2} \left (a y^{\prime }+b \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.641 |
|
| 24211 |
\begin{align*}
y^{\prime } x&=y+a \sqrt {y^{2}+b^{2} x^{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
18.663 |
|
| 24212 |
\begin{align*}
y^{\prime }&=\frac {a x +b}{y^{n}+d} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.682 |
|
| 24213 |
\begin{align*}
y^{\prime }&=\frac {x +1+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.685 |
|
| 24214 |
\begin{align*}
4 x -y+2+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.698 |
|
| 24215 |
\begin{align*}
y^{\prime }&=x \sqrt {1-y^{2}} \\
y \left (0\right ) &= {\frac {9}{10}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.702 |
|
| 24216 |
\begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.713 |
|
| 24217 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\left (2 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.734 |
|
| 24218 | \begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 18.736 |
|
| 24219 |
\begin{align*}
y \left (y^{2}+x^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.740 |
|
| 24220 |
\begin{align*}
x -y-1+\left (4 y+x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.804 |
|
| 24221 |
\begin{align*}
y^{\prime }&=\frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (x -1\right ) \cosh \left (\frac {1}{x +1}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.805 |
|
| 24222 |
\begin{align*}
2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.820 |
|
| 24223 |
\begin{align*}
3 x^{2}-y^{2}-\left (y x -\frac {x^{3}}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.833 |
|
| 24224 |
\begin{align*}
\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.833 |
|
| 24225 |
\begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.859 |
|
| 24226 |
\begin{align*}
y^{\prime } y&=a \cos \left (\lambda x \right ) y+1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
18.863 |
|
| 24227 |
\begin{align*}
x^{2} {y^{\prime }}^{3}+y \left (x^{2} y+1\right ) {y^{\prime }}^{2}+y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
18.877 |
|
| 24228 |
\begin{align*}
y^{\prime } x&=y+a \sqrt {y^{2}-b^{2} x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.906 |
|
| 24229 |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y-4 \,{\mathrm e}^{-2 x^{2}} x^{4}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y+4 x^{2} {\mathrm e}^{-2 x^{2}}+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 y \,{\mathrm e}^{-x^{2}}-8 \,{\mathrm e}^{-x^{2}}\right ) x}{-8 y+4 x^{2} {\mathrm e}^{-x^{2}}-8} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.913 |
|
| 24230 |
\begin{align*}
x^{2} y^{\prime }&=\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.927 |
|
| 24231 |
\begin{align*}
y^{\prime }&=-\frac {-y^{3}-y+2 y^{2} \ln \left (x \right )-\ln \left (x \right )^{2} y^{3}-1+3 y \ln \left (x \right )-3 \ln \left (x \right )^{2} y^{2}+\ln \left (x \right )^{3} y^{3}}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.944 |
|
| 24232 |
\begin{align*}
x +y-1+\left (-x +y-5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.958 |
|
| 24233 |
\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*} |
✗ |
✓ |
✓ |
✗ |
18.967 |
|
| 24234 |
\begin{align*}
x +3 y+\left (3 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.030 |
|
| 24235 |
\begin{align*}
\frac {1}{x^{2}-y x +y^{2}}&=\frac {y^{\prime }}{2 y^{2}-y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.040 |
|
| 24236 |
\begin{align*}
x +y-2-\left (x -4 y-2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.047 |
|
| 24237 |
\begin{align*}
2 y^{2}+4 x^{2}-x y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.068 |
|
| 24238 | \begin{align*}
\cos \left (x +y^{2}\right )+3 y+\left (2 y \cos \left (x +y^{2}\right )+3 x \right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 19.078 |
|
| 24239 |
\begin{align*}
y^{\prime } y+\frac {a \left (6 x -1\right ) y}{2 x}&=-\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
19.083 |
|
| 24240 |
\begin{align*}
x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.108 |
|
| 24241 |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y\right ) x +\ln \left (y\right )-x -1+x \ln \left (x \right )+\ln \left (x \right )+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.126 |
|
| 24242 |
\begin{align*}
x^{4}-4 y^{2} x^{2}-y^{4}+4 x^{3} y y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.141 |
|
| 24243 |
\begin{align*}
y^{\prime }&=\frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.163 |
|
| 24244 |
\begin{align*}
\frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.196 |
|
| 24245 |
\begin{align*}
\left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.197 |
|
| 24246 |
\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*} |
✓ |
✓ |
✓ |
✗ |
19.242 |
|
| 24247 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.247 |
|
| 24248 |
\begin{align*}
x {y^{\prime }}^{2}&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.283 |
|
| 24249 |
\begin{align*}
-y+y^{\prime } x&=x^{k} y^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.288 |
|
| 24250 |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.291 |
|
| 24251 |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+x \ln \left (x \right )^{2}+2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.293 |
|
| 24252 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) y^{\prime \prime }+\left (a_{1} x +b_{1} \right ) y^{\prime }+\left (a_{0} x +b_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.309 |
|
| 24253 |
\begin{align*}
x -3 y+2+3 \left (x +3 y-4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.360 |
|
| 24254 |
\begin{align*}
y^{\prime }&=\frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.388 |
|
| 24255 |
\begin{align*}
x -2 y+3+2 \left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.398 |
|
| 24256 |
\begin{align*}
-\left (4 k^{2}-\left (-p^{2}+1\right ) \sinh \left (x \right )^{2}\right ) y+4 \cosh \left (x \right ) \sinh \left (x \right ) y^{\prime }+4 \sinh \left (x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.406 |
|
| 24257 | \begin{align*}
\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=2\). | ✓ | ✓ | ✓ | ✓ | 19.421 |
|
| 24258 |
\begin{align*}
y^{\prime }&=\frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.479 |
|
| 24259 |
\begin{align*}
y^{\prime }&=\sqrt {x^{2}-y}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.487 |
|
| 24260 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +b \lambda -2 a b -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}-b \left (b +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.509 |
|
| 24261 |
\begin{align*}
\left (x -\sqrt {y^{2}+x^{2}}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.522 |
|
| 24262 |
\begin{align*}
y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.543 |
|
| 24263 |
\begin{align*}
x {y^{\prime }}^{2}+y^{\prime } y+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
19.590 |
|
| 24264 |
\begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.592 |
|
| 24265 |
\begin{align*}
y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.645 |
|
| 24266 |
\begin{align*}
y^{2}+\left (x \sqrt {y^{2}-x^{2}}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.661 |
|
| 24267 |
\begin{align*}
2 y^{2} x^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.698 |
|
| 24268 |
\begin{align*}
y^{\prime }&=t y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
19.727 |
|
| 24269 |
\begin{align*}
x^{2}+y^{2}+\left (a x y+y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
19.754 |
|
| 24270 |
\begin{align*}
\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.764 |
|
| 24271 |
\begin{align*}
x^{\prime }&=-t x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.829 |
|
| 24272 |
\begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.966 |
|
| 24273 |
\begin{align*}
y^{\prime }&=\frac {x -2 y}{2 x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
19.972 |
|
| 24274 |
\begin{align*}
y+2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
19.978 |
|
| 24275 |
\begin{align*}
y^{\prime }&=\frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
20.019 |
|
| 24276 |
\begin{align*}
\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
20.063 |
|
| 24277 | \begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 20.078 |
|
| 24278 |
\begin{align*}
-p \left (1+p \right ) y+2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
20.084 |
|
| 24279 |
\begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.098 |
|
| 24280 |
\begin{align*}
y^{\prime }&=\frac {3 y x^{2}}{x^{3}+2 y^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.110 |
|
| 24281 |
\begin{align*}
y^{\prime }&=\frac {3 x -y+1}{-x +3 y+5} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
20.131 |
|
| 24282 |
\begin{align*}
x +y+1-\left (-3+x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.138 |
|
| 24283 |
\begin{align*}
\left (3-x -y\right ) y^{\prime }&=1+x -3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.139 |
|
| 24284 |
\begin{align*}
y^{\prime \prime }&=f \left (a x +b y, y^{\prime }\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
20.201 |
|
| 24285 |
\begin{align*}
y^{\prime }+y \sin \left (x \right )&=2 x \,{\mathrm e}^{\cos \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.203 |
|
| 24286 |
\begin{align*}
y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
20.256 |
|
| 24287 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
20.315 |
|
| 24288 |
\begin{align*}
x -3 y+3+\left (3 x +y+9\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
20.315 |
|
| 24289 |
\begin{align*}
x {y^{\prime }}^{2}+y^{\prime } y+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
20.323 |
|
| 24290 |
\begin{align*}
y^{\prime }&=x -y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
20.332 |
|
| 24291 |
\begin{align*}
\left (\sqrt {y x}-1\right ) x y^{\prime }-\left (\sqrt {y x}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.385 |
|
| 24292 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
20.423 |
|
| 24293 |
\begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.469 |
|
| 24294 |
\begin{align*}
y^{\prime } y&=\left (a x +3 b \right ) y+c \,x^{3}-b \,x^{2} a -2 b^{2} x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
20.477 |
|
| 24295 |
\begin{align*}
\left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.486 |
|
| 24296 |
\begin{align*}
y^{\prime }&=\frac {y \left ({\mathrm e}^{-\frac {x^{2}}{2}} x y+{\mathrm e}^{-\frac {x^{2}}{4}} x +2 y^{2} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2 y \,{\mathrm e}^{-\frac {x^{2}}{4}}+2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
20.500 |
|
| 24297 | \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*} | ✓ | ✓ | ✓ | ✓ | 20.525 |
|
| 24298 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+a \sin \left (\lambda x \right ) y-a \tan \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
20.542 |
|
| 24299 |
\begin{align*}
2 t +\left (y-3 t \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.555 |
|
| 24300 |
\begin{align*}
\left (x^{2}-y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.595 |
|