| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 23201 |
\begin{align*}
3 y^{2}-x +\left (2 y^{3}-6 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.014 |
|
| 23202 |
\begin{align*}
x y^{\prime }&=y+x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.022 |
|
| 23203 |
\begin{align*}
y^{\prime }&=y^{{2}/{3}}+a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.023 |
|
| 23204 |
\begin{align*}
y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.026 |
|
| 23205 |
\begin{align*}
y y^{\prime }&=b \cos \left (x +c \right )+a y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.037 |
|
| 23206 |
\begin{align*}
-y-3 x y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.038 |
|
| 23207 |
\begin{align*}
y^{\prime }&=\sin \left (x \right )+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.043 |
|
| 23208 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=5-y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.046 |
|
| 23209 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.046 |
|
| 23210 |
\begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.050 |
|
| 23211 |
\begin{align*}
y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.050 |
|
| 23212 |
\begin{align*}
2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.051 |
|
| 23213 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{2 \lambda x} y^{3}+b \,{\mathrm e}^{\lambda x} y^{2}+c y+d \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.052 |
|
| 23214 |
\begin{align*}
x^{\prime \prime }+x+x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.056 |
|
| 23215 |
\begin{align*}
x y^{\prime \prime }-\left (a +b \right ) \left (x +1\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.059 |
|
| 23216 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.062 |
|
| 23217 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.069 |
|
| 23218 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.076 |
|
| 23219 |
\begin{align*}
y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.085 |
|
| 23220 |
\begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.086 |
|
| 23221 |
\begin{align*}
\left (t +3\right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (t +3\right ) \cos \left (t +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.089 |
|
| 23222 |
\begin{align*}
{y^{\prime }}^{2}&=\left (4 y+1\right ) \left (y^{\prime }-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.090 |
|
| 23223 |
\begin{align*}
y&=3 x y^{\prime }-7 {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.090 |
|
| 23224 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.093 |
|
| 23225 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.099 |
|
| 23226 |
\begin{align*}
y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.102 |
|
| 23227 |
\begin{align*}
\left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.102 |
|
| 23228 |
\begin{align*}
y^{4}-{y^{\prime }}^{4}-y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.106 |
|
| 23229 |
\begin{align*}
x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.107 |
|
| 23230 |
\begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.109 |
|
| 23231 |
\begin{align*}
-\left (\left (1+2 n \right )^{2}-4 x^{2}\right ) y+4 x y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.124 |
|
| 23232 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
9.124 |
|
| 23233 |
\begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.132 |
|
| 23234 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.140 |
|
| 23235 |
\begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| 23236 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| 23237 |
\begin{align*}
y^{\prime }+y-y^{{1}/{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.157 |
|
| 23238 |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.160 |
|
| 23239 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.165 |
|
| 23240 |
\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*} |
✓ |
✓ |
✓ |
✗ |
9.166 |
|
| 23241 |
\begin{align*}
y^{\prime }&=\frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.171 |
|
| 23242 |
\begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )-7 y x +7&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.172 |
|
| 23243 |
\begin{align*}
y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.172 |
|
| 23244 |
\begin{align*}
\frac {-x y^{\prime }+y}{\left (x +y\right )^{2}}+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.172 |
|
| 23245 |
\begin{align*}
1+y^{2}&=\frac {y^{\prime }}{x^{3} \left (x -1\right )} \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.173 |
|
| 23246 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+\lambda f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.173 |
|
| 23247 |
\begin{align*}
y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.174 |
|
| 23248 |
\begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.174 |
|
| 23249 |
\begin{align*}
x^{3} y^{\prime }-\cos \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
9.174 |
|
| 23250 |
\begin{align*}
y^{4}-y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.175 |
|
| 23251 |
\begin{align*}
{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.180 |
|
| 23252 |
\begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.181 |
|
| 23253 |
\begin{align*}
y^{\prime }&=\frac {\sin \left (\frac {y}{x}\right ) \left (y+2 x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )\right )}{2 \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.181 |
|
| 23254 |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {5 \pi }{4} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
9.183 |
|
| 23255 |
\begin{align*}
\left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime }&=\frac {T}{t \sqrt {t^{2}-T^{2}}}-t \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.184 |
|
| 23256 |
\begin{align*}
y^{\prime }&=\frac {\left (x +1\right )^{2}-2 y}{2 y} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.193 |
|
| 23257 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.199 |
|
| 23258 |
\begin{align*}
y^{\prime }&=3 \sqrt {y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.203 |
|
| 23259 |
\begin{align*}
y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.205 |
|
| 23260 |
\begin{align*}
y+3 x +x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.210 |
|
| 23261 |
\begin{align*}
y^{\prime }&=-\frac {1296 y}{216+216 x^{2}+216 x^{3}-1296 y-846 y^{7}-1944 y^{4}-1728 y^{3}+1080 x y^{3}+1152 x y^{4}+216 x y^{2}-315 y^{9}-432 y x -2376 y^{2}-648 x^{2} y^{2}-126 y^{10}-8 y^{12}-36 y^{11}-882 y^{6}-648 x^{2} y-216 x^{2} y^{4}+1080 y^{5} x +594 x y^{6}+72 y^{8} x +216 y^{7} x -570 y^{8}-324 x^{2} y^{3}-612 y^{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.214 |
|
| 23262 |
\begin{align*}
\frac {\ln \left (1+{y^{\prime }}^{2}\right )}{2}-\ln \left (y^{\prime }\right )-x +2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.217 |
|
| 23263 |
\begin{align*}
x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.219 |
|
| 23264 |
\begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.227 |
|
| 23265 |
\begin{align*}
\left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.233 |
|
| 23266 |
\begin{align*}
\left (-1+3 x +y\right )^{2} y^{\prime }-\left (-1+2 y\right ) \left (4 y+6 x -3\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.238 |
|
| 23267 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.242 |
|
| 23268 |
\begin{align*}
x y^{\prime }+y&=a \left (y x +1\right ) \\
y \left (\frac {1}{a}\right ) &= -a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.249 |
|
| 23269 |
\begin{align*}
\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.250 |
|
| 23270 |
\begin{align*}
\frac {y}{x -1}+\frac {x y^{\prime }}{y+1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| 23271 |
\begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| 23272 |
\begin{align*}
y \left (1+2 y x \right )-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| 23273 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=y^{6} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.259 |
|
| 23274 |
\begin{align*}
y+x^{3}+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.264 |
|
| 23275 |
\begin{align*}
\left (y-4 x -1\right )^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.270 |
|
| 23276 |
\begin{align*}
y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.272 |
|
| 23277 |
\begin{align*}
x y^{\prime }&=2 x -y \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.273 |
|
| 23278 |
\begin{align*}
\left (x^{2}+6 x y^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.274 |
|
| 23279 |
\begin{align*}
x y^{\prime }&=2 y^{2}-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.275 |
|
| 23280 |
\begin{align*}
x y^{\prime }+y&=2 x \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.275 |
|
| 23281 |
\begin{align*}
\cos \left (x \right ) y^{\prime }-y^{4}-y \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.279 |
|
| 23282 |
\begin{align*}
x y^{\prime }&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.282 |
|
| 23283 |
\begin{align*}
y^{\prime }&=y^{3}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.285 |
|
| 23284 |
\begin{align*}
T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \\
T \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.295 |
|
| 23285 |
\begin{align*}
y^{\prime }&=\frac {x +1+2 \sqrt {1+4 x^{2} y}\, x^{3}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.301 |
|
| 23286 |
\begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.303 |
|
| 23287 |
\begin{align*}
y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.310 |
|
| 23288 |
\begin{align*}
x y^{\prime }+2 y&=6 x^{2} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.314 |
|
| 23289 |
\begin{align*}
y {y^{\prime }}^{2}+2 a x y^{\prime }-a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.316 |
|
| 23290 |
\begin{align*}
\sin \left (x \right ) \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.326 |
|
| 23291 |
\begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.329 |
|
| 23292 |
\begin{align*}
y^{\prime }&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.335 |
|
| 23293 |
\begin{align*}
y-y^{\prime }&=x y^{\prime }+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.337 |
|
| 23294 |
\begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.340 |
|
| 23295 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.343 |
|
| 23296 |
\begin{align*}
1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.344 |
|
| 23297 |
\begin{align*}
y&=-a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.349 |
|
| 23298 |
\begin{align*}
x +y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.351 |
|
| 23299 |
\begin{align*}
y^{\prime }&=\frac {\sin \left (\frac {y}{x}\right ) \left (y+2 x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )\right )}{2 \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.352 |
|
| 23300 |
\begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.352 |
|