2.3.229 Problems 22801 to 22900

Table 2.1001: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22801	2841	\begin{align*} x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.010
22802	25022	\begin{align*} y^{\prime }&=\frac {1}{\left (y+t \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	12.025
22803	2819	\begin{align*} z^{\prime \prime }+z^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	12.026
22804	1710	\begin{align*} y+\left (2 x +\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.027
22805	4873	\begin{align*} x^{2} y^{\prime }&=\left (1+2 x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	12.029
22806	23941	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	12.037
22807	17928	\begin{align*} y \left (1+\sqrt {1+x^{2} y^{4}}\right )+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	12.055
22808	4816	\begin{align*} y^{\prime } x&=y-x \cot \left (\frac {y}{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✗	12.059
22809	12486	\begin{align*} x^{2} y^{\prime \prime }+\left (x -2 x^{2} f \left (x \right )\right ) y^{\prime }+\left (x^{2} \left (1+f \left (x \right )^{2}-f^{\prime }\left (x \right )\right )-f \left (x \right ) x -v^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	12.064
22810	13422	\begin{align*} y^{\prime }&=\lambda \arcsin \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arcsin \left (x \right )^{n} \\ \end{align*}	✓	✓	✓	✓	12.064
22811	14039	\begin{align*} \left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )+\sqrt {1+x^{2}+y^{2}}\, \left (-y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	12.065
22812	2520	\begin{align*} y^{\prime }&={\mathrm e}^{t}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	12.079
22813	4692	\begin{align*} y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	12.080
22814	10280	\begin{align*} c y^{\prime }&=\frac {a x +b y^{2}}{r \,x^{2}} \\ \end{align*}	✓	✓	✓	✗	12.083
22815	6921	\begin{align*} y+7+\left (2 x +y+3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	12.084
22816	2501	\begin{align*} y^{\prime } t&=y+\sqrt {t^{2}+y^{2}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	12.085
22817	15621	\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	12.086
22818	4733	\begin{align*} y^{\prime }&=\sqrt {a +b \cos \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	12.092
22819	20261	\begin{align*} x^{2}+3 y^{2}-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	12.094
22820	5320	\begin{align*} \left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime }&=a^{2} x y \\ \end{align*}	✓	✓	✓	✗	12.095
22821	17263	\begin{align*} 2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.098
22822	8705	\begin{align*} -y+y^{\prime } x&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	12.103
22823	1198	\begin{align*} y^{\prime }&=\frac {-a x +b y}{b x -c y} \\ \end{align*}	✓	✓	✓	✗	12.104
22824	13811	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime \prime }+b y^{\prime }-6 y&=0 \\ \end{align*}	✗	✓	✓	✗	12.107
22825	5942	\begin{align*} \left (b x +a \right ) y+y^{\prime }+2 y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	12.108
22826	14014	\begin{align*} y^{\prime } x -a y+b y^{2}&=c \,x^{2 a} \\ \end{align*}	✓	✓	✓	✗	12.112
22827	21362	\begin{align*} x +2 y-1+3 \left (x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	12.116
22828	10417	\begin{align*} y^{\prime } y^{\prime \prime }+y^{n}&=0 \\ \end{align*}	✓	✓	✓	✗	12.122
22829	17104	\begin{align*} y^{\prime }&=y^{3}-y^{2} \\ \end{align*}	✓	✓	✓	✓	12.128
22830	7706	\begin{align*} y^{\prime } x +3 y&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	12.129
22831	7012	\begin{align*} y^{\prime } x&=x +y+{\mathrm e}^{\frac {y}{x}} x \\ \end{align*}	✓	✓	✓	✗	12.135
22832	4796	\begin{align*} y^{\prime } x&=y \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	12.138
22833	16156	\begin{align*} y y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	12.138
22834	1652	\begin{align*} y^{\prime }&=\frac {y^{2}-3 y x -5 x^{2}}{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	12.142
22835	2328	\begin{align*} 3 y^{\prime } t&=y \cos \left (t \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	12.153
22836	22359	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	12.158
22837	18580	\begin{align*} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	12.168
22838	2938	\begin{align*} \left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	12.170
22839	20221	\begin{align*} x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.173
22840	19073	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.179
22841	1657	\begin{align*} y^{\prime }&=\frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	12.181
22842	5257	\begin{align*} \left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	12.185
22843	7469	\begin{align*} \sin \left (x \right ) y^{2}+\left (\frac {1}{x}-\frac {y}{x}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	12.194
22844	24214	\begin{align*} \left (-y^{2}+x^{2}+1\right ) y-x \left (x^{2}-y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	12.194
22845	19706	\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \\ \end{align*}	✓	✓	✓	✓	12.196
22846	23849	\begin{align*} 2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	12.201
22847	7254	\begin{align*} y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	12.206
22848	19094	\begin{align*} \left (x \left (x +y\right )+a^{2}\right ) y^{\prime }&=y \left (x +y\right )+b^{2} \\ \end{align*}	✓	✓	✓	✓	12.212
22849	12222	\begin{align*} y^{\prime }&=-\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{x^{2}-y^{2}-1}}}{-y^{2}-2 y x -x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{x^{2}-y^{2}-1}}} \\ \end{align*}	✓	✓	✓	✗	12.219
22850	17888	\begin{align*} \sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.219
22851	26169	\begin{align*} 3 x^{2}-8 y x +2 y^{2}-\left (4 x^{2}-4 y x +3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	12.220
22852	1655	\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}	✓	✓	✓	✓	12.227
22853	24208	\begin{align*} y \left (y^{3}-x \right )+x \left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	12.233
22854	4189	\begin{align*} y y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	12.239
22855	3777	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	12.240
22856	16297	\begin{align*} y^{\prime }&=\frac {y}{x}+\frac {x^{2}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	12.240
22857	1597	\begin{align*} x +y y^{\prime }&=0 \\ y \left (3\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	12.245
22858	9205	\begin{align*} y^{\prime }&=\frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \\ \end{align*}	✓	✓	✓	✗	12.256
22859	11352	\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*}	✗	✓	✓	✗	12.258
22860	6903	\begin{align*} 2 \,{\mathrm e}^{\frac {x}{y}} y+\left (y-2 \,{\mathrm e}^{\frac {x}{y}} x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.261
22861	4992	\begin{align*} x^{4} y^{\prime }&=\left (x^{3}+y\right ) y \\ \end{align*}	✓	✓	✓	✓	12.266
22862	22522	\begin{align*} r^{2} \sin \left (t \right )&=\left (2 r \cos \left (t \right )+10\right ) r^{\prime } \\ \end{align*}	✓	✓	✓	✓	12.270
22863	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*}	✓	✗	✗	✗	12.278
22864	19527	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	12.279
22865	5039	\begin{align*} y y^{\prime }+x \,{\mathrm e}^{-x} \left (1+y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	12.282
22866	18591	\begin{align*} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	12.285
22867	4081	\begin{align*} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.286
22868	5028	\begin{align*} y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )&=y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right ) \\ \end{align*}	✓	✓	✓	✗	12.293
22869	5922	\begin{align*} c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	12.303
22870	14448	\begin{align*} 2 y x -3+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	12.303
22871	22963	\begin{align*} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\ \end{align*}	✓	✓	✓	✓	12.308
22872	12083	\begin{align*} y^{\prime }&=\frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \\ \end{align*}	✓	✓	✓	✗	12.309
22873	23064	\begin{align*} r^{\prime } \left (\sin \left (\theta \right )-m \cos \left (\theta \right )\right )+r \left (\cos \left (\theta \right )+m \sin \left (\theta \right )\right )&=0 \\ \end{align*}	✓	✓	✓	✓	12.315
22874	22601	\begin{align*} x^{2} y^{3}+2 x y^{2}+y+\left (x^{3} y^{2}-2 x^{2} y+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✓	12.318
22875	17961	\begin{align*} y^{\prime }-\cos \left (x \right ) y&=y^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	12.321
22876	12598	\begin{align*} y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}-\frac {\left (a x +b \right ) y}{4 x \left (x -1\right )^{2}} \\ \end{align*}	✗	✓	✓	✗	12.336
22877	13409	\begin{align*} y^{\prime }&=\sin \left (\lambda x \right ) a y^{2}+b \sin \left (\lambda x \right ) \cos \left (\lambda x \right )^{n} \\ \end{align*}	✓	✓	✓	✗	12.336
22878	12250	\begin{align*} y^{\prime }&=-\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-18 y^{8}+216 x^{3}-1296 y+594 x y^{6}+594 y^{7}+4428 y^{5}+1728 y^{3}-648 x y^{3}+1080 x y^{5}-1296 y^{2}-1296 y x +72 y^{8} x +216 y^{7} x +2484 y^{6}+2808 y^{4}-216 x^{2} y^{4}-648 y^{2} x^{2}-432 y^{4} x -1944 x y^{2}-648 x^{2} y-324 x^{2} y^{3}-315 y^{9}-126 y^{10}-8 y^{12}-36 y^{11}} \\ \end{align*}	✓	✓	✓	✗	12.348
22879	2498	\begin{align*} y^{\prime }&=k \left (a -y\right ) \left (b -y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	12.355
22880	20680	\begin{align*} \left (x +2 y^{3}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	12.357
22881	7509	\begin{align*} y^{\prime }+\frac {y}{x}&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	12.370
22882	12039	\begin{align*} y^{\prime }&=\frac {-4 y x +x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \\ \end{align*}	✓	✓	✓	✓	12.382
22883	6895	\begin{align*} 2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	12.383
22884	6989	\begin{align*} y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	12.383
22885	3554	\begin{align*} 2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	12.390
22886	9657	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+2 z \\ z^{\prime }&=z-x \\ \end{align*}	✓	✓	✓	✗	12.394
22887	12089	\begin{align*} y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\ \end{align*}	✗	✓	✓	✗	12.395
22888	4508	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	12.397
22889	5188	\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	12.399
22890	13485	\begin{align*} y^{\prime }&=\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}-\frac {g^{\prime }\left (x \right )}{f \left (x \right )} \\ \end{align*}	✗	✓	✓	✗	12.420
22891	3657	\begin{align*} y^{\prime }+\frac {\tan \left (x \right ) y}{2}&=2 y^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	12.424
22892	14892	\begin{align*} y^{\prime } x&=k y \\ \end{align*}	✓	✓	✓	✓	12.426
22893	19329	\begin{align*} \left (x +y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	12.432
22894	4827	\begin{align*} y^{\prime } x&=x +y+{\mathrm e}^{\frac {y}{x}} x \\ \end{align*}	✓	✓	✓	✗	12.438
22895	13416	\begin{align*} y^{\prime }&=y^{2}+a \lambda +b \lambda +2 a b +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}+b \left (\lambda -b \right ) \cot \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✗	✗	12.448
22896	14826	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	12.448
22897	21833	\begin{align*} 2-x -y+\left (x +y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.450
22898	17923	\begin{align*} 8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.454
22899	11364	\begin{align*} y^{\prime }-\frac {1+y^{2}}{{| y+\sqrt {1+y}|} \left (x +1\right )^{{3}/{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	12.458
22900	24213	\begin{align*} \left (x^{3}-y^{5}\right ) y-x \left (x^{3}+y^{5}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	12.468