2.3.55 Problems 5401 to 5500

Table 2.693: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5401	25978	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \end {array} \]	✓	✓	✓	✓	0.490
5402	26196	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-4 \left (x +1\right ) y^{\prime }+4 y&=0 \end {array} \]	✓	✓	✓	✓	0.490
5403	871	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+a x y^{\prime }&=b c \,x^{2} \end {array} \]	✓	✓	✓	✓	0.491
5404	4499	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-a x y^{\prime }+a y&=0 \end {array} \]	✓	✓	✓	✓	0.491
5405	7821	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y&=0 \end {array} \]	✓	✓	✓	✓	0.491
5406	10028	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c&=b y \end {array} \]	✓	✓	✓	✓	0.491
5407	14384	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y^{\prime } x&=0 \end {array} \]	✓	✓	✓	✓	0.491
5408	15189	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \end {array} \]	✓	✓	✓	✓	0.491
5409	18919	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y&=0 \end {array} \]	✓	✓	✓	✓	0.491
5410	19586	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \end {array} \]	✓	✓	✓	✓	0.491
5411	23825	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \end {array} \]	✓	✓	✓	✓	0.491
5412	25442	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }+{y^{\prime }}^{2}&=x \left (x +y\right ) \end {array} \]	✓	✓	✓	✓	0.491
5413	26602	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \end {array} \]	✓	✓	✓	✓	0.491
5414	28153	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \end {array} \]	✓	✓	✓	✓	0.491
5415	495	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \end {array} \]	✓	✓	✓	✗	0.492
5416	1457	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (1+2 y\right ) y^{\prime }+y \left (-1+y\right )&=0 \end {array} \]	✓	✓	✓	✓	0.492
5417	4173	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x&=0 \end {array} \]	✓	✓	✓	✓	0.492
5418	5906	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \end {array} \]	✓	✓	✓	✗	0.492
5419	7211	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y&=0 \end {array} \]	✓	✓	✓	✗	0.492
5420	8933	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right )&=0 \end {array} \]	✓	✓	✓	✓	0.492
5421	14817	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+a y y^{\prime }-a x&=0 \end {array} \]	✓	✓	✓	✓	0.492
5422	18869	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-a y y^{\prime }-a x&=0 \end {array} \]	✓	✓	✓	✓	0.492
5423	25112	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \end {array} \]	✓	✓	✓	✓	0.492
5424	25248	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y y^{\prime } x +y^{2} \ln \left (a y\right )&=0 \end {array} \]	✓	✓	✓	✗	0.492
5425	453	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+2 y x&=0 \end {array} \]	✓	✓	✓	✓	0.493
5426	3616	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2}&=0 \end {array} \]	✓	✓	✓	✓	0.493
5427	4169	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3}&=0 \end {array} \]	✓	✓	✓	✓	0.493
5428	4497	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+y^{2} y^{\prime } x +y^{3}&=0 \end {array} \]	✓	✓	✓	✓	0.493
5429	5393	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \end {array} \]	✓	✓	✓	✓	0.493
5430	9311	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+y^{4} x^{4}&=0 \end {array} \]	✓	✓	✓	✓	0.493
5431	10771	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \end {array} \]	✓	✓	✓	✗	0.493
5432	12985	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \end {array} \]	✓	✓	✓	✗	0.493
5433	17597	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \end {array} \]	✓	✓	✓	✓	0.493
5434	18662	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&={\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \end {array} \]	✓	✓	✓	✓	0.493
5435	21290	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 {y^{\prime }}^{2}+y^{\prime } x -2 y&=0 \end {array} \]	✓	✓	✓	✗	0.493
5436	22819	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y&=0 \end {array} \]	✓	✓	✓	✓	0.493
5437	26826	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \end {array} \]	✓	✓	✓	✓	0.493
5438	293	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right )&=0 \end {array} \]	✓	✓	✓	✓	0.494
5439	468	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \end {array} \]	✓	✓	✓	✓	0.494
5440	844	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 {y^{\prime }}^{2}+4 y^{\prime } x +x^{2}-y&=0 \end {array} \]	✓	✓	✓	✓	0.494
5441	1488	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 {y^{\prime }}^{2}&=9 x \end {array} \]	✓	✓	✓	✓	0.494
5442	2549	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y}&=0 \end {array} \]	✓	✓	✓	✓	0.494
5443	3115	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y}&=0 \end {array} \]	✓	✓	✓	✓	0.494
5444	3928	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \end {array} \]	✓	✓	✓	✓	0.494
5445	4531	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \end {array} \]	✓	✓	✓	✓	0.494
5446	5633	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \end {array} \]	✓	✓	✗	✗	0.494
5447	5964	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}&=a \end {array} \]	✓	✓	✓	✓	0.494
5448	10296	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}&=\left (a -x \right )^{2} \end {array} \]	✓	✓	✓	✓	0.494
5449	14924	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}&=y \end {array} \]	✓	✓	✓	✓	0.494
5450	16772	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+x -2 y&=0 \end {array} \]	✓	✓	✓	✓	0.494
5451	21523	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y^{\prime }&=y \end {array} \]	✓	✓	✓	✓	0.494
5452	25255	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \end {array} \]	✓	✓	✓	✓	0.494
5453	26037	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-2 y^{\prime }-y&=0 \end {array} \]	✓	✓	✓	✓	0.494
5454	28205	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+4 y^{\prime }-2 y&=0 \end {array} \]	✓	✓	✓	✓	0.494
5455	1010	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y^{\prime } x -y&=0 \end {array} \]	✓	✓	✓	✓	0.495
5456	3854	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \end {array} \]	✓	✓	✓	✓	0.495
5457	10353	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y y^{\prime }+a&=0 \end {array} \]	✓	✓	✓	✗	0.495
5458	15187	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-y y^{\prime }+a&=0 \end {array} \]	✓	✓	✓	✓	0.495
5459	18649	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-y y^{\prime }+a x&=0 \end {array} \]	✓	✓	✓	✓	0.495
5460	18926	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y y^{\prime }-x^{2}&=0 \end {array} \]	✓	✓	✓	✓	0.495
5461	21219	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y y^{\prime }+x^{3}&=0 \end {array} \]	✓	✓	✓	✓	0.495
5462	24666	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-y y^{\prime }+a y&=0 \end {array} \]	✓	✓	✓	✓	0.495
5463	3150	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \end {array} \]	✓	✓	✓	✓	0.496
5464	3339	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b&=0 \end {array} \]	✓	✓	✓	✓	0.496
5465	10118	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \end {array} \]	✓	✓	✓	✗	0.496
5466	10234	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y&=0 \end {array} \]	✓	✓	✓	✓	0.496
5467	14688	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (3 x -y\right ) y^{\prime }+y&=0 \end {array} \]	✓	✓	✓	✓	0.496
5468	14920	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (a +b x -y\right ) y^{\prime }-b y&=0 \end {array} \]	✓	✓	✓	✓	0.496
5469	18429	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-2 y y^{\prime }+a&=0 \end {array} \]	✓	✓	✓	✓	0.496
5470	18820	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+2 y y^{\prime }-x&=0 \end {array} \]	✓	✓	✓	✓	0.496
5471	20489	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-2 y y^{\prime }+a x&=0 \end {array} \]	✓	✓	✓	✓	0.496
5472	23824	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \end {array} \]	✓	✓	✓	✓	0.496
5473	25079	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2}&=0 \end {array} \]	✓	✓	✓	✓	0.496
5474	1730	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \end {array} \]	✓	✓	✓	✓	0.497
5475	2259	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-a y y^{\prime }+b&=0 \end {array} \]	✓	✓	✓	✓	0.497
5476	3883	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+a y y^{\prime }+b x&=0 \end {array} \]	✓	✓	✓	✓	0.497
5477	7661	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \end {array} \]	✓	✓	✓	✗	0.497
5478	8036	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \end {array} \]	✓	✓	✓	✗	0.497
5479	8628	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \end {array} \]	✓	✓	✓	✓	0.497
5480	12981	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) {y^{\prime }}^{2}&=y \end {array} \]	✓	✓	✓	✗	0.497
5481	13158	\(\left [\begin {array}{ccc} 4 & -3 & 1 \\ 2 & -1 & 1 \\ 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.497
5482	14599	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a -x \right ) {y^{\prime }}^{2}+y y^{\prime }-b&=0 \end {array} \]	✓	✓	✓	✓	0.497
5483	16670	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \end {array} \]	✓	✓	✓	✓	0.497
5484	18916	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \end {array} \]	✓	✓	✓	✓	0.497
5485	21945	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \end {array} \]	✓	✓	✓	✓	0.497
5486	23806	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x +5\right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \end {array} \]	✓	✓	✓	✓	0.497
5487	26822	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x {y^{\prime }}^{2}&=\left (a -3 x \right )^{2} \end {array} \]	✓	✓	✓	✓	0.497
5488	26969	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \end {array} \]	✓	✓	✓	✓	0.497
5489	27686	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x {y^{\prime }}^{2}-3 y y^{\prime }+3&=0 \end {array} \]	✓	✓	✓	✓	0.497
5490	1008	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x {y^{\prime }}^{2}+4 y y^{\prime }&=1 \end {array} \]	✓	✓	✓	✓	0.498
5491	4006	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x {y^{\prime }}^{2}+4 y y^{\prime }-y^{4}&=0 \end {array} \]	✓	✓	✓	✗	0.498
5492	4012	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 \left (-x +2\right ) {y^{\prime }}^{2}+1&=0 \end {array} \]	✓	✓	✓	✗	0.498
5493	8127	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6}&=0 \end {array} \]	✓	✓	✓	✓	0.498
5494	15186	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}&=a^{2} \end {array} \]	✓	✓	✓	✓	0.498
5495	17649	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}&=y^{2} \end {array} \]	✓	✓	✓	✓	0.498
5496	22845	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+x^{2}-y^{2}&=0 \end {array} \]	✓	✓	✓	✗	0.498
5497	27963	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \end {array} \]	✓	✓	✓	✓	0.498
5498	3581	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+y^{2}-y^{4}&=0 \end {array} \]	✓	✓	✓	✓	0.499
5499	4016	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right )&=0 \end {array} \]	✓	✓	✓	✓	0.499
5500	8072	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y&=0 \end {array} \]	✓	✓	✓	✓	0.499