2.3.234 Problems 23301 to 23400

Table 2.1017: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
23301	3030	\begin{align*} y^{\prime } x +y \left (1+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	12.980
23302	5328	\begin{align*} x \left (x^{3}+y^{5}\right ) y^{\prime }&=\left (x^{3}-y^{5}\right ) y \\ \end{align*}	✓	✓	✓	✗	12.989
23303	11977	\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*}	✗	✓	✓	✗	12.990
23304	17152	\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \\ \end{align*}	✓	✓	✓	✓	12.990
23305	25830	\begin{align*} y^{\prime }&=\frac {y \left (\cos \left (x \right ) x +\sin \left (x \right )-1\right )}{3 x -3 x \sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	12.998
23306	4887	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\ \end{align*}	✗	✓	✓	✗	13.001
23307	11933	\begin{align*} y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 a x +a^{2}+4 y} \\ \end{align*}	✓	✓	✓	✓	13.002
23308	7336	\begin{align*} 2 x -y \sin \left (2 x \right )&=\left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	13.007
23309	25883	\begin{align*} 2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.010
23310	4929	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	13.011
23311	11940	\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}	✓	✓	✓	✗	13.012
23312	7681	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	13.028
23313	4726	\begin{align*} y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\ \end{align*}	✗	✓	✓	✓	13.031
23314	4987	\begin{align*} x^{2} \left (1-x \right ) y^{\prime }&=x \left (2-x \right ) y-y^{2} \\ \end{align*}	✓	✓	✓	✓	13.037
23315	13739	\begin{align*} y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y&=0 \\ \end{align*}	✗	✓	✗	✗	13.040
23316	4928	\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	13.050
23317	15055	\begin{align*} 3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.055
23318	6914	\begin{align*} x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.057
23319	4863	\begin{align*} 3 y^{\prime } x&=\left (3 \ln \left (x \right ) y^{3} x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	13.061
23320	13494	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+h \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	13.063
23321	751	\begin{align*} y^{\prime } x +6 y&=3 x y^{{4}/{3}} \\ \end{align*}	✓	✓	✓	✓	13.075
23322	5059	\begin{align*} \left (x -y\right ) y^{\prime }&=\left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	13.083
23323	24154	\begin{align*} x^{2}+2 y^{2}-y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	13.083
23324	11942	\begin{align*} y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +4 a y+b^{2}-4 c} \\ \end{align*}	✓	✓	✓	✓	13.086
23325	4308	\begin{align*} x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.087
23326	21039	\begin{align*} x^{\prime }&=t^{2} x^{4}+1 \\ x \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	13.087
23327	2901	\begin{align*} x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.088
23328	22551	\begin{align*} y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x -y\right )} \\ \end{align*}	✓	✓	✓	✓	13.089
23329	1815	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{4} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	13.100
23330	3022	\begin{align*} y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	13.110
23331	20805	\begin{align*} y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-\cot \left (x \right ) y&=\sin \left (x \right )^{2} \\ \end{align*}	✗	✓	✓	✗	13.114
23332	17262	\begin{align*} y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t}&=0 \\ \end{align*}	✓	✓	✓	✗	13.124
23333	18493	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\ y \left (0\right ) &= -\sqrt {3} \\ \end{align*}	✓	✓	✗	✓	13.124
23334	2904	\begin{align*} 6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	13.128
23335	16976	\begin{align*} 3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.158
23336	22388	\begin{align*} y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\ \end{align*}	✓	✓	✓	✓	13.159
23337	13684	\begin{align*} y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	13.161
23338	2985	\begin{align*} y y^{\prime } x&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	13.170
23339	4879	\begin{align*} x^{2} y^{\prime }+2+x y \left (4+y x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	13.174
23340	12055	\begin{align*} y^{\prime }&=\frac {y x +x +y^{2}}{\left (x -1\right ) \left (x +y\right )} \\ \end{align*}	✓	✓	✓	✗	13.187
23341	13464	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}-f \left (x \right ) \left (a \,{\mathrm e}^{\lambda x}+b \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✗	✗	✗	13.201
23342	24942	\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}	✓	✓	✓	✓	13.208
23343	4958	\begin{align*} 2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	13.216
23344	12257	\begin{align*} y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{-x^{2}}+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x \\ \end{align*}	✓	✓	✓	✗	13.219
23345	14002	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.223
23346	729	\begin{align*} \left (x +y\right ) y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	13.234
23347	21341	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	13.256
23348	5428	\begin{align*} {y^{\prime }}^{2}+y^{\prime } y^{2} x +y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	13.259
23349	6190	\begin{align*} -y+2 y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	13.265
23350	13752	\begin{align*} y^{\prime \prime } x +a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	13.267
23351	1624	\begin{align*} y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\ y \left (3\right ) &= -7 \\ \end{align*}	✓	✓	✓	✗	13.272
23352	24955	\begin{align*} y^{\prime }&=t^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	13.272
23353	13659	\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*}	✓	✓	✓	✗	13.277
23354	4993	\begin{align*} x^{4} y^{\prime }+a^{2}+y^{2} x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	13.283
23355	24330	\begin{align*} 2 y+x \left (x^{2} \ln \left (y\right )-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.283
23356	23124	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	13.288
23357	2906	\begin{align*} x +y+4&=\left (2 x +2 y-1\right ) y^{\prime } \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	13.289
23358	13427	\begin{align*} y^{\prime }&=y^{2}+\lambda \arccos \left (x \right )^{n} y-a^{2}+a \lambda \arccos \left (x \right )^{n} \\ \end{align*}	✓	✓	✓	✓	13.289
23359	2907	\begin{align*} 2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime }&=0 \\ y \left (3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	13.309
23360	4763	\begin{align*} y^{\prime } x&=a x +b y \\ \end{align*}	✓	✓	✓	✓	13.309
23361	5529	\begin{align*} x^{3} {y^{\prime }}^{2}&=a \\ \end{align*}	✓	✓	✓	✓	13.309
23362	13523	\begin{align*} y y^{\prime }-y&=\frac {A}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	13.310
23363	12099	\begin{align*} y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{3} \cos \left (2 y\right ) \ln \left (x \right )+x^{3} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\ \end{align*}	✗	✓	✓	✓	13.316
23364	19770	\begin{align*} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✗	13.319
23365	20284	\begin{align*} 2 y^{\prime }-y \sec \left (x \right )&=y^{3} \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	13.319
23366	4956	\begin{align*} x \left (1-2 x \right ) y^{\prime }&=4 x -\left (4 x +1\right ) y+y^{2} \\ \end{align*}	✓	✓	✓	✓	13.333
23367	4830	\begin{align*} y^{\prime } x +\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	13.343
23368	4230	\begin{align*} y^{\prime } x&=2 y \left (-1+y\right ) \\ y \left (\frac {1}{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	13.354
23369	13443	\begin{align*} y^{\prime }&=y^{2}+\lambda x \operatorname {arccot}\left (x \right )^{n} y+\operatorname {arccot}\left (x \right )^{n} \lambda \\ \end{align*}	✓	✓	✓	✗	13.358
23370	8728	\begin{align*} 2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.362
23371	8403	\begin{align*} y^{\prime }&=x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	13.366
23372	12165	\begin{align*} y^{\prime }&=-\frac {i \left (32 i x +64+64 y^{4}+32 y^{2} x^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 y^{2} x^{4}+x^{6}\right )}{128 y} \\ \end{align*}	✗	✗	✗	✗	13.371
23373	21595	\begin{align*} x +2 y+3+\left (2 x +4 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.375
23374	17959	\begin{align*} 2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	13.381
23375	12171	\begin{align*} y^{\prime }&=\frac {y^{2} \left (-2 y+2 x^{2}+2 x^{2} y+x^{4} y\right )}{x^{3} \left (x^{2}-y+x^{2} y\right )} \\ \end{align*}	✓	✓	✓	✗	13.384
23376	11966	\begin{align*} y^{\prime }&=\frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x} \\ \end{align*}	✓	✓	✓	✗	13.385
23377	1231	\begin{align*} x +y+\left (x +2 y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	13.386
23378	12102	\begin{align*} y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+\ln \left (x \right ) x^{2}}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\ \end{align*}	✗	✓	✓	✓	13.397
23379	5536	\begin{align*} x^{4} {y^{\prime }}^{2}+y^{\prime } y^{2} x -y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	13.399
23380	17271	\begin{align*} t^{3}+y^{3}-t y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.405
23381	15385	\begin{align*} \frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	13.409
23382	7491	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	13.410
23383	8364	\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= \frac {\sqrt {3}}{2} \\ \end{align*}	✓	✓	✓	✗	13.416
23384	21303	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✗	13.416
23385	6943	\begin{align*} y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.419
23386	6910	\begin{align*} 3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.420
23387	1160	\begin{align*} y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	13.423
23388	15619	\begin{align*} y^{\prime }&=y^{3} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	13.431
23389	20259	\begin{align*} -y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	13.442
23390	4970	\begin{align*} x^{3} y^{\prime }&=y \left (y+x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	13.447
23391	13311	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n} \\ \end{align*}	✗	✗	✗	✗	13.459
23392	2956	\begin{align*} y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	13.461
23393	12048	\begin{align*} y^{\prime }&=\frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	13.467
23394	1205	\begin{align*} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	13.483
23395	13468	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}} \\ \end{align*}	✓	✗	✗	✗	13.483
23396	4849	\begin{align*} \left (a -x \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\ \end{align*}	✓	✓	✓	✓	13.484
23397	9148	\begin{align*} x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\ \end{align*}	✓	✓	✓	✓	13.485
23398	24323	\begin{align*} x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.488
23399	7228	\begin{align*} \left (y x +x \right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	13.492
23400	7146	\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*}	✗	✓	✓	✗	13.495