2.3.231 Problems 23001 to 23100

Table 2.1005: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
23001	2987	\begin{align*} t x^{\prime }+x \left (1-x^{2} t^{4}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	13.031
23002	24299	\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\ \end{align*}	✓	✓	✓	✗	13.054
23003	11490	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-y \sqrt {-1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	13.063
23004	5328	\begin{align*} x \left (x^{3}+y^{5}\right ) y^{\prime }&=\left (x^{3}-y^{5}\right ) y \\ \end{align*}	✓	✓	✓	✗	13.071
23005	23724	\begin{align*} x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	13.071
23006	17064	\begin{align*} y^{\prime }&=t y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	13.074
23007	1205	\begin{align*} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	13.075
23008	13661	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y^{2}-2 a \,b^{3} {\mathrm e}^{\left (\lambda +3 \mu \right ) x}-{\mathrm e}^{\mu x} b \mu \\ \end{align*}	✓	✓	✓	✗	13.078
23009	1815	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{4} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	13.079
23010	23865	\begin{align*} 2 y \ln \left (x \right ) \ln \left (y\right )+x \left (\ln \left (x \right )^{2}+\ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.081
23011	21039	\begin{align*} x^{\prime }&=t^{2} x^{4}+1 \\ x \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	13.087
23012	5099	\begin{align*} \left (-3 y-2 x +5\right ) y^{\prime }+1-2 x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	13.099
23013	12123	\begin{align*} y^{\prime }&=\frac {y+x^{2} \ln \left (x \right )^{3}+2 x^{2} \ln \left (x \right )^{2} y+x^{2} \ln \left (x \right ) y^{2}}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	13.107
23014	4237	\begin{align*} y y^{\prime } x&=\sqrt {y^{2}-9} \\ y \left ({\mathrm e}^{4}\right ) &= 5 \\ \end{align*}	✓	✓	✓	✗	13.112
23015	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
23016	16344	\begin{align*} 3 x y^{3}-y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	13.118
23017	5586	\begin{align*} \left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	13.136
23018	17877	\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	13.147
23019	20002	\begin{align*} \left (y y^{\prime }+x n \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✗	✓	13.147
23020	1656	\begin{align*} \left (-y+y^{\prime } x \right ) \left (\ln \left (y\right )-\ln \left (x \right )\right )&=x \\ \end{align*}	✓	✓	✓	✓	13.149
23021	8291	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✗	✓	✓	✗	13.153
23022	19733	\begin{align*} \sqrt {t^{2}+T}&=T^{\prime } \\ \end{align*}	✓	✓	✓	✗	13.154
23023	25734	\begin{align*} 2 y^{\prime \prime }-3 y^{2}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	13.154
23024	21423	\begin{align*} 3 x^{2} y+\left (y^{4}-x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.155
23025	14000	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	13.174
23026	19781	\begin{align*} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=r y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✗	13.177
23027	5097	\begin{align*} \left (4-x -3 y\right ) y^{\prime }+3-x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	13.180
23028	11342	\begin{align*} y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	13.180
23029	1624	\begin{align*} y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\ y \left (3\right ) &= -7 \\ \end{align*}	✓	✓	✓	✗	13.181
23030	9197	\begin{align*} y^{\prime }&=\frac {x +2 y}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	13.184
23031	19721	\begin{align*} \frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	13.184
23032	26210	\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	13.196
23033	23667	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	13.203
23034	17969	\begin{align*} \frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	13.205
23035	24316	\begin{align*} 3 x -2 y+1+\left (3 x -2 y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.215
23036	729	\begin{align*} \left (x +y\right ) y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	13.221
23037	12043	\begin{align*} y^{\prime }&=\frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \\ \end{align*}	✓	✓	✓	✓	13.226
23038	7413	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	13.231
23039	22399	\begin{align*} 2 x +2 y+1+\left (x +y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.231
23040	5089	\begin{align*} \left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\ \end{align*}	✓	✓	✓	✓	13.233
23041	21398	\begin{align*} y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	13.238
23042	5093	\begin{align*} \left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime }&=2 \,{\mathrm e}^{-2 x} x -\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \\ \end{align*}	✓	✓	✓	✗	13.242
23043	1160	\begin{align*} y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	13.243
23044	19964	\begin{align*} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.246
23045	16351	\begin{align*} \sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.258
23046	24203	\begin{align*} x y^{2}+y-x +x \left (y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.294
23047	8310	\begin{align*} y y^{\prime }&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	13.301
23048	22405	\begin{align*} 2+3 x y^{2}-4 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.310
23049	8720	\begin{align*} y^{\prime }&=\frac {y}{x +y} \\ \end{align*}	✓	✓	✓	✓	13.311
23050	17050	\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	13.316
23051	22966	\begin{align*} {\mathrm e}^{y} \left (y^{\prime } x +1\right )&=5 \\ \end{align*}	✓	✓	✓	✓	13.317
23052	12766	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+\ln \left (x \right )+2 y^{\prime } x -y-2 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	13.319
23053	26166	\begin{align*} \left (x +y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	13.321
23054	23177	\begin{align*} y^{\prime }&=\left (1-y\right ) \left (-\frac {1}{t \ln \left (t \right )}-\frac {3}{100}+\frac {3 y}{100}\right ) \\ \end{align*}	✓	✓	✓	✓	13.338
23055	12158	\begin{align*} y^{\prime }&=\frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \\ \end{align*}	✓	✓	✓	✗	13.346
23056	4240	\begin{align*} x^{2}-y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	13.350
23057	5543	\begin{align*} y {y^{\prime }}^{2}&=a^{2} x \\ \end{align*}	✓	✓	✓	✓	13.352
23058	5924	\begin{align*} \left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	13.365
23059	25008	\begin{align*} y^{\prime }&=\frac {t^{2}+y^{2}}{t y} \\ y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	13.369
23060	13804	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (x^{n} a b +a c \,x^{n -1}+b^{2} x^{2}+2 b x c +c^{2}-c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	13.371
23061	5204	\begin{align*} 3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	13.374
23062	17875	\begin{align*} y^{\prime } x&=2 x -y \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	13.375
23063	19103	\begin{align*} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	13.375
23064	19199	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	13.375
23065	21555	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	13.395
23066	4680	\begin{align*} y^{\prime }&=a x y^{2} \\ \end{align*}	✓	✓	✓	✓	13.398
23067	19674	\begin{align*} \left (t^{2}-x^{2}\right ) x^{\prime }&=t x \\ \end{align*}	✓	✓	✓	✓	13.401
23068	24212	\begin{align*} y \left (1+y^{2}\right )+x \left (-1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.415
23069	26163	\begin{align*} x^{2}+y^{2}-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	13.415
23070	18599	\begin{align*} y y^{\prime } x&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	13.416
23071	13370	\begin{align*} y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+\lambda \sin \left (\lambda x \right )^{3} \\ \end{align*}	✓	✓	✗	✗	13.422
23072	24232	\begin{align*} 2 x^{5} y^{\prime }&=y \left (3 x^{4}+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	13.436
23073	10019	\begin{align*} p^{\prime }&=a p-b p^{2} \\ p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\ \end{align*}	✓	✓	✓	✓	13.441
23074	4334	\begin{align*} y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.448
23075	12350	\begin{align*} y^{\prime \prime }-\left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) \left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right )}{f \left (x \right )}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {v^{2} {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	13.449
23076	23963	\begin{align*} {\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.449
23077	14440	\begin{align*} y^{2}+3+\left (2 y x -4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.450
23078	2899	\begin{align*} x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.451
23079	13977	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	13.460
23080	6573	\begin{align*} y^{\prime } y^{\prime \prime }&=x y^{2}+x^{2} y y^{\prime } \\ \end{align*}	✗	✗	✗	✗	13.479
23081	21806	\begin{align*} x^{3}-y^{3}+y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	13.483
23082	21594	\begin{align*} y^{\prime }&=\frac {x +y+1}{x +y+2} \\ \end{align*}	✓	✓	✓	✓	13.486
23083	14015	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.487
23084	1709	\begin{align*} y^{\prime }+2 y x&=-\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	13.500
23085	11581	\begin{align*} \left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	13.508
23086	6830	\begin{align*} \left (-x +y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	13.515
23087	19804	\begin{align*} \sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	13.523
23088	14244	\begin{align*} x^{\prime }&=t -x^{2} \\ \end{align*}	✓	✓	✓	✗	13.535
23089	5923	\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	13.539
23090	4391	\begin{align*} y&=y^{\prime } x -x^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✗	✗	13.543
23091	11837	\begin{align*} {y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}&=0 \\ \end{align*}	✓	✓	✓	✗	13.550
23092	19746	\begin{align*} y^{\prime }&=1+\frac {2 y}{x -y} \\ \end{align*}	✓	✓	✓	✓	13.553
23093	6881	\begin{align*} x&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\ \end{align*}	✓	✓	✓	✓	13.554
23094	6985	\begin{align*} \left (x -\cos \left (y\right )\right ) y^{\prime }+\tan \left (y\right )&=0 \\ y \left (1\right ) &= \frac {\pi }{6} \\ \end{align*}	✓	✓	✓	✓	13.554
23095	6857	\begin{align*} -y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	13.559
23096	12292	\begin{align*} y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	13.593
23097	14473	\begin{align*} \left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	13.594
23098	2858	\begin{align*} \tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.599
23099	13053	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	13.599
23100	13648	\begin{align*} 9 y^{\prime }&=-x^{m} \left (a \,x^{-m +1}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{-m +1}+b \right )^{-\lambda -2} \\ \end{align*}	✗	✗	✗	✗	13.600