2.3.231 Problems 23001 to 23100

Table 2.1035: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
23001	4652	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	8.440
23002	5006	\begin{align*} x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1} y&=0 \\ \end{align*}	✓	✓	✓	✗	8.441
23003	8874	\begin{align*} L y^{\prime }+R y&=E \,{\mathrm e}^{i \omega x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	8.445
23004	6929	\begin{align*} x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	8.446
23005	19279	\begin{align*} x y^{\prime }&=y+2 x \,{\mathrm e}^{-\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✓	8.448
23006	17144	\begin{align*} t y^{\prime }+y&=t \\ \end{align*}	✓	✓	✓	✓	8.460
23007	4954	\begin{align*} 2 \left (-x^{2}+1\right ) y^{\prime }&=\sqrt {-x^{2}+1}+\left (x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	8.462
23008	19091	\begin{align*} \left (-x +y\right ) \sqrt {x^{2}+1}\, y^{\prime }&=\left (1+y^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	8.462
23009	13649	\begin{align*} x y^{\prime }&=a \,x^{4} y^{3}+\left (b \,x^{2}-1\right ) y+c x \\ \end{align*}	✓	✓	✓	✗	8.464
23010	26411	\begin{align*} \left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \\ \end{align*}	✓	✓	✓	✓	8.464
23011	18476	\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\ \end{align*}	✓	✓	✓	✓	8.467
23012	22739	\begin{align*} y^{\prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	8.468
23013	22177	\begin{align*} \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	8.474
23014	4902	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\ \end{align*}	✓	✓	✓	✓	8.478
23015	8679	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ \end{align*}	✓	✓	✓	✓	8.479
23016	730	\begin{align*} 2 x y y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	8.484
23017	8061	\begin{align*} 2 \left (y+1\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	8.484
23018	4264	\begin{align*} y-\left (x +x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.488
23019	26919	\begin{align*} y^{\prime }&=x^{2}-y^{2}+\frac {8 x}{y} \\ y \left (3\right ) &= -1 \\ \end{align*}	✗	✗	✗	✗	8.492
23020	11590	\begin{align*} x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}+x^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	8.494
23021	20959	\begin{align*} x^{\prime }&=\mu -x^{3} \\ \end{align*}	✓	✓	✓	✓	8.496
23022	18504	\begin{align*} y^{\prime }&=\frac {6-{\mathrm e}^{x}}{3+2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	8.498
23023	5158	\begin{align*} 2 x y y^{\prime }+a +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	8.499
23024	3462	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+4 y x&=\left (-x^{2}+1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	8.500
23025	5881	\begin{align*} a k \,x^{-1+k} y+2 a \,x^{k} y^{\prime }+2 y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	8.502
23026	13977	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	8.502
23027	5860	\begin{align*} -2 \left (1+\cos \left (x \right )\right ) \sec \left (x \right ) y-\left (2+3 \cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	8.504
23028	26166	\begin{align*} \left (x +y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	8.505
23029	8347	\begin{align*} y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	8.510
23030	27258	\begin{align*} 2 x y^{\prime }+y&=y^{2} \sqrt {x -x^{2} y^{2}} \\ \end{align*}	✓	✓	✓	✗	8.512
23031	5012	\begin{align*} \left (x -\sqrt {x^{2}+1}\right ) y^{\prime }&=y+\sqrt {1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	8.513
23032	9161	\begin{align*} y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	8.514
23033	4947	\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }&=c y^{2} \\ \end{align*}	✓	✓	✓	✓	8.520
23034	5324	\begin{align*} \left (x +2 y+2 x^{2} y^{3}+x y^{4}\right ) y^{\prime }+\left (1+y^{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	8.520
23035	27460	\begin{align*} \frac {x y^{\prime }}{y}+2 x y \ln \left (x \right )+1&=0 \\ \end{align*}	✓	✓	✓	✓	8.520
23036	20315	\begin{align*} \left (2 x +2 y+3\right ) y^{\prime }&=x +y+1 \\ \end{align*}	✓	✓	✓	✓	8.525
23037	27242	\begin{align*} y+\sqrt {y x}&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	8.526
23038	5024	\begin{align*} y^{\prime } \sqrt {b \,x^{4}+a \,x^{2}+1}+\sqrt {1+a y^{2}+b y^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	8.532
23039	15499	\begin{align*} 2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	8.534
23040	13906	\begin{align*} x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	8.535
23041	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*}	✓	✓	✓	✗	8.536
23042	9530	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	8.538
23043	5011	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	8.539
23044	22361	\begin{align*} 3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.542
23045	22548	\begin{align*} x^{2} y+\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.542
23046	14440	\begin{align*} y^{2}+3+\left (2 y x -4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.546
23047	14898	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	8.553
23048	22375	\begin{align*} x^{3} {\mathrm e}^{2 x^{2}+3 y^{2}}-y^{3} {\mathrm e}^{-x^{2}-2 y^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.553
23049	17953	\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}	✓	✓	✓	✓	8.554
23050	22804	\begin{align*} x y^{\prime }&=x^{2} y^{2}-y+1 \\ \end{align*}	✓	✓	✓	✓	8.556
23051	3672	\begin{align*} y^{\prime }&=\left (4 x +y+2\right )^{2} \\ \end{align*}	✓	✓	✓	✓	8.557
23052	14463	\begin{align*} \left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.565
23053	9987	\begin{align*} y^{\prime }&=\frac {\cos \left (y\right ) \sec \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	8.570
23054	4929	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	8.575
23055	12263	\begin{align*} y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (x -1\right ) \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✗	8.575
23056	15397	\begin{align*} y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\ \end{align*}	✓	✓	✓	✓	8.579
23057	4327	\begin{align*} x y^{2}+x -2 y+3+\left (x^{2} y-2 y-2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	8.580
23058	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*}	✓	✓	✓	✗	8.581
23059	13642	\begin{align*} y^{\prime }&=a y^{3}+3 a b x y^{2}-b -2 a \,b^{3} x^{3} \\ \end{align*}	✓	✓	✓	✗	8.583
23060	4928	\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	8.584
23061	17527	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	8.593
23062	8289	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	8.598
23063	13492	\begin{align*} x^{2} y^{\prime }&=x^{4} f \left (x \right ) y^{2}+1 \\ \end{align*}	✗	✗	✗	✗	8.598
23064	24894	\begin{align*} y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	8.602
23065	12305	\begin{align*} y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	8.611
23066	4813	\begin{align*} x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	8.612
23067	26346	\begin{align*} {y^{\prime }}^{2}-2 y y^{\prime }&=y^{2} \left ({\mathrm e}^{x}-1\right ) \\ \end{align*}	✓	✓	✓	✓	8.613
23068	4987	\begin{align*} x^{2} \left (1-x \right ) y^{\prime }&=x \left (2-x \right ) y-y^{2} \\ \end{align*}	✓	✓	✓	✓	8.618
23069	5174	\begin{align*} \left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	8.618
23070	14019	\begin{align*} x y^{\prime }+y+{\mathrm e}^{x} x^{4} y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	8.623
23071	4751	\begin{align*} x y^{\prime }+x +y&=0 \\ \end{align*}	✓	✓	✓	✓	8.625
23072	10257	\begin{align*} y^{\prime \prime }+{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✓	8.628
23073	6208	\begin{align*} \left (a -1\right ) \left (a +b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	8.631
23074	7880	\begin{align*} x -2 \sin \left (y\right )+3+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.631
23075	5351	\begin{align*} \left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	8.634
23076	25646	\begin{align*} y^{\prime }&=y^{2}-t \\ \end{align*}	✓	✓	✓	✗	8.634
23077	10121	\begin{align*} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	8.635
23078	26691	\begin{align*} y^{\prime \prime }-\alpha ^{2} s y&=0 \\ y \left (0\right ) &= -\frac {1}{s} \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	8.636
23079	12209	\begin{align*} y^{\prime }&=-\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 x^{2} y^{2}+x^{3} y^{3}}{32 y x} \\ \end{align*}	✓	✓	✓	✗	8.639
23080	8166	\begin{align*} y^{\prime }&=25+y^{2} \\ \end{align*}	✓	✓	✓	✓	8.641
23081	5199	\begin{align*} 2 x^{3} y y^{\prime }+a +3 x^{2} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	8.646
23082	10025	\begin{align*} y y^{\prime }-y&=x \\ \end{align*}	✓	✓	✓	✗	8.649
23083	14534	\begin{align*} y^{2} {\mathrm e}^{2 x}-2 x +y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	8.650
23084	21376	\begin{align*} \left (x +y^{2}\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	8.652
23085	2846	\begin{align*} \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.668
23086	15614	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	8.669
23087	5505	\begin{align*} {y^{\prime }}^{2} x^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	8.671
23088	1164	\begin{align*} y^{\prime }&=\frac {x^{2}-3 y^{2}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	8.683
23089	5045	\begin{align*} y y^{\prime }&=a x +b x y^{2} \\ \end{align*}	✓	✓	✓	✓	8.683
23090	17068	\begin{align*} \frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.683
23091	12200	\begin{align*} y^{\prime }&=\frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 y^{5} x +y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\ \end{align*}	✓	✗	✓	✗	8.685
23092	5591	\begin{align*} 3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	8.691
23093	4970	\begin{align*} x^{3} y^{\prime }&=y \left (x^{2}+y\right ) \\ \end{align*}	✓	✓	✓	✓	8.696
23094	12166	\begin{align*} y^{\prime }&=\frac {2 x^{2}-4 x^{3} y+1+y^{2} x^{4}+x^{6} y^{3}-3 x^{5} y^{2}+3 x^{4} y-x^{3}}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	8.705
23095	19317	\begin{align*} x y^{\prime }+y+3 x^{3} y^{4} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.707
23096	25819	\begin{align*} x y^{\prime }&=4 y \\ \end{align*}	✓	✓	✓	✓	8.710
23097	27499	\begin{align*} x y^{\prime }-2 y+x y^{2} \left (2 x y^{\prime }+y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	8.717
23098	22390	\begin{align*} x -4 y+\left (3 x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	8.720
23099	25828	\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	8.720
23100	18495	\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\ y \left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	8.722