2.3.75 Problems 7401 to 7500

Table 2.733: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7401	10687	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+2 y y^{\prime }&=0\\ y \left (0\right )&=2\\ \end {array} \]	✓	✓	✓	✗	0.666
7402	14730	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 t \cos \left (y\right )^{2}\\ y \left (0\right )&=\frac {\pi }{4}\\ \end {array} \]	✓	✓	✓	✓	0.666
7403	15245	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y}\\ y \left (1\right )&=0\\ \end {array} \]	✓	✓	✓	✓	0.666
7404	16170	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2} \left (1+y\right )\\ y \left (0\right )&=3\\ \end {array} \]	✓	✓	✓	✓	0.666
7405	18114	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sqrt {y}+\left (x +1\right ) y^{\prime }&=0\\ y \left (0\right )&=1\\ \end {array} \]	✓	✓	✗	✗	0.666
7406	18920	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x^{2}}\\ y \left (0\right )&=0\\ \end {array} \]	✓	✓	✓	✓	0.666
7407	20391	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{x^{2}}}{y^{2}}\\ y \left (0\right )&=1\\ \end {array} \]	✓	✓	✓	✓	0.666
7408	6024	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right )\\ y \left (0\right )&=1\\ \end {array} \]	✓	✓	✓	✗	0.667
7409	6251	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y-2 t y\\ y \left (0\right )&=3\\ \end {array} \]	✓	✓	✓	✓	0.667
7410	7167	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{{1}/{3}} \end {array} \]	✓	✓	✓	✗	0.667
7411	10145	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{{1}/{3}}\\ y \left (0\right )&=0\\ \end {array} \]	✓	✓	✓	✓	0.667
7412	10527	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (x -3\right ) \left (1+y\right )^{{2}/{3}} \end {array} \]	✓	✓	✓	✗	0.667
7413	10634	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x y^{3} \end {array} \]	✓	✓	✓	✗	0.667
7414	10847	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x y^{3}\\ y \left (0\right )&=1\\ \end {array} \]	✓	✓	✓	✗	0.667
7415	10886	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x y^{3}\\ y \left (0\right )&={\frac {1}{2}}\\ \end {array} \]	✓	✓	✓	✗	0.667
7416	16136	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x y^{3}\\ y \left (0\right )&=2\\ \end {array} \]	✓	✓	✓	✓	0.667
7417	16634	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{2}-3 y+2\\ y \left (0\right )&={\frac {3}{2}}\\ \end {array} \]	✓	✓	✓	✓	0.667
7418	18234	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+\sin \left (x \right )-y&=0 \end {array} \]	✓	✓	✓	✓	0.667
7419	18669	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+t x&={\mathrm e}^{x} \end {array} \]	✓	✓	✓	✓	0.667
7420	19657	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime }&=t y-y \end {array} \]	✓	✓	✓	✓	0.667
7421	26028	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t&={\mathrm e}^{t} y^{\prime }+y \ln \left (t \right ) \end {array} \]	✓	✓	✓	✓	0.667
7422	840	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x x^{\prime }+t^{2} x&=\sin \left (t \right ) \end {array} \]	✓	✓	✓	✓	0.668
7423	2293	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 r&=r^{\prime }-\theta ^{3} \end {array} \]	✓	✓	✓	✓	0.668
7424	3744	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y-{\mathrm e}^{3 x}&=0 \end {array} \]	✓	✓	✓	✓	0.668
7425	3951	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{x}+2 x +1 \end {array} \]	✓	✓	✓	✓	0.668
7426	4017	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} r^{\prime }+r \tan \left (\theta \right )&=\sec \left (\theta \right ) \end {array} \]	✓	✓	✓	✓	0.668
7427	4067	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +2 y&=\frac {1}{x^{3}} \end {array} \]	✓	✓	✓	✓	0.668
7428	6189	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t +y+1-y^{\prime }&=0 \end {array} \]	✓	✓	✓	✗	0.668
7429	9218	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \end {array} \]	✓	✓	✓	✓	0.668
7430	10707	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x^{\prime }+2 x&=5 y^{3} \end {array} \]	✓	✓	✓	✗	0.668
7431	10884	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +3 y+3 x^{2}&=\frac {\sin \left (x \right )}{x} \end {array} \]	✓	✓	✓	✗	0.668
7432	13191	\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.668
7433	14127	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime }-x^{2} y&=\left (x +1\right ) \sqrt {-x^{2}+1} \end {array} \]	✓	✓	✓	✓	0.668
7434	17756	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x}\\ y \left (1\right )&={\mathrm e}-1\\ \end {array} \]	✓	✓	✓	✓	0.668
7435	17757	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y-{\mathrm e}^{-x}&=0\\ y \left (0\right )&={\frac {4}{3}}\\ \end {array} \]	✓	✓	✓	✓	0.668
7436	21023	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime }+3 t x&=t^{4} \ln \left (t \right )+1\\ x \left (1\right )&=0\\ \end {array} \]	✓	✓	✓	✓	0.668
7437	21515	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {3 y}{x}+2&=3 x\\ y \left (1\right )&=1\\ \end {array} \]	✓	✓	✓	✓	0.668
7438	25973	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=2 x \cos \left (x \right )^{2}\\ y \left (\frac {\pi }{4}\right )&=-\frac {15 \sqrt {2}\, \pi ^{2}}{32}\\ \end {array} \]	✓	✓	✓	✓	0.668
7439	27841	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=x \sin \left (x \right )\\ y \left (\frac {\pi }{2}\right )&=2\\ \end {array} \]	✓	✓	✓	✓	0.668
7440	1460	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}}&=x\\ y \left (0\right )&=2\\ \end {array} \]	✓	✓	✓	✓	0.669
7441	3828	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1&=0 \end {array} \]	✓	✓	✓	✓	0.669
7442	6078	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=\frac {x}{y^{2}} \end {array} \]	✓	✓	✓	✗	0.669
7443	6268	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {3 y}{x}&=x^{2} \end {array} \]	✓	✓	✓	✗	0.669
7444	7783	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x\\ x \left (0\right )&=x_{0}\\ \end {array} \]	✓	✓	✓	✓	0.669
7445	9270	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime }&=\alpha \left (1-u\right )-\beta u \end {array} \]	✓	✓	✓	✓	0.669
7446	10479	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime }&=0 \end {array} \]	✓	✓	✓	✗	0.669
7447	10632	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{{10}/{3}}-2 y+y^{\prime } x&=0 \end {array} \]	✓	✓	✓	✗	0.669
7448	14801	\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.669
7449	16507	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \,{\mathrm e}^{y x}+2 x +\left (x \,{\mathrm e}^{y x}-2 y\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.669
7450	17485	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y x&=0 \end {array} \]	✓	✓	✓	✓	0.669
7451	25816	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (2 y x +\cos \left (y\right )\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.669
7452	27797	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +y \cos \left (y x \right )+\left (x \cos \left (y x \right )-2 y\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.669
7453	27961	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \theta r^{\prime }+3 r-\theta -1&=0 \end {array} \]	✓	✓	✓	✓	0.669
7454	158	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +3+\left (x^{2}-1\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✗	0.670
7455	2370	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2 y\right ) y^{\prime }+2 x +y&=0 \end {array} \]	✓	✓	✓	✓	0.670
7456	2596	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.670
7457	7197	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{t} \left (y-t \right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.670
7458	10856	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {t y^{\prime }}{y}+1+\ln \left (y\right )&=0 \end {array} \]	✓	✓	✓	✗	0.670
7459	14077	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta }&=0 \end {array} \]	✓	✓	✓	✓	0.670
7460	14426	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.670
7461	16088	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.670
7462	16506	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +y^{2}-\cos \left (x +y\right )+\left (2 y x -\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.670
7463	17829	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +\frac {y}{1+y^{2} x^{2}}+\left (\frac {x}{1+y^{2} x^{2}}-2 y\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.670
7464	21213	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {2}{\sqrt {-x^{2}+1}}+y \cos \left (y x \right )+\left (x \cos \left (y x \right )-\frac {1}{y^{{1}/{3}}}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.670
7465	22901	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {1}{x}+2 x y^{2}+\left (2 x^{2} y-\cos \left (y\right )\right ) y^{\prime }&=0\\ y \left (1\right )&=\pi \\ \end {array} \]	✓	✓	✓	✓	0.670
7466	26929	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0\\ y \left (1\right )&=1\\ \end {array} \]	✓	✓	✓	✓	0.670
7467	27383	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{t} y+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0\\ y \left (0\right )&=-1\\ \end {array} \]	✓	✓	✓	✓	0.670
7468	27798	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{t} x+1+\left ({\mathrm e}^{t}-1\right ) x^{\prime }&=0\\ x \left (1\right )&=1\\ \end {array} \]	✓	✓	✓	✓	0.670
7469	499	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{2}+\left (\frac {1}{x}-\frac {y}{x}\right ) y^{\prime }&=0\\ y \left (\pi \right )&=1\\ \end {array} \]	✓	✓	✓	✓	0.671
7470	1073	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \tan \left (y\right )-2+\left (x \sec \left (y\right )^{2}+\frac {1}{y}\right ) y^{\prime }&=0\\ y \left (0\right )&=1\\ \end {array} \]	✓	✓	✓	✓	0.671
7471	2583	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+2 y x -x^{2} y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7472	2747	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 x^{2} y+6 x^{3} y^{2}+4 x y^{2}+\left (2 x^{3}+3 x^{4} y+3 x^{2} y\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7473	4000	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +\frac {y}{x}+\left (y x -1\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7474	7166	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✗	0.671
7475	7209	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2 y\right ) y^{\prime }+2 x +y&=0 \end {array} \]	✓	✓	✓	✓	0.671
7476	10419	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+2 y x -x^{2} y^{\prime }&=0 \end {array} \]	✗	✓	✓	✗	0.671
7477	10448	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \sin \left (x \right )+4 y+y^{\prime } x&=0 \end {array} \]	✓	✓	✓	✓	0.671
7478	10718	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{2}-y+y^{\prime } x&=0 \end {array} \]	✓	✓	✓	✓	0.671
7479	10896	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✗	0.671
7480	10994	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✗	0.671
7481	14680	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4}-x +y-y^{\prime } x&=0 \end {array} \]	✓	✓	✓	✓	0.671
7482	16034	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{2}+2 y+4 x^{2}+\left (2 y x +x \right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7483	16126	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+2 y x -x^{2} y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7484	17354	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{3}+1+\left (3 y^{2} x^{2}-\frac {1}{y}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7485	17397	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{2}-6 y x +\left (3 y x -4 x^{2}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7486	17447	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+2 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7487	24547	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3+y+y x +\left (3+x +y x \right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7488	25110	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +2 y+2 x^{3} y+4 y^{2} x^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7489	26548	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t x x^{\prime }+t^{2}-x^{2}&=0 \end {array} \]	✓	✓	✓	✓	0.671
7490	26573	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y-4 x -1\right )^{2}-y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.671
7491	3835	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y}{x}&=x^{3} y^{2} \end {array} \]	✓	✓	✓	✓	0.672
7492	6455	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t +x+2\right ) x^{\prime }+3 t -x-6&=0 \end {array} \]	✗	✗	✗	✗	0.672
7493	14807	\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.672
7494	16509	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.672
7495	16758	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \end {array} \]	✓	✓	✓	✓	0.672
7496	16850	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \end {array} \]	✓	✓	✓	✗	0.672
7497	17433	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +y^{2}-x^{2} y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.672
7498	17821	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2}-y^{2}-\left (y x -\frac {x^{3}}{y}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	0.672
7499	18233	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y^{2}-y x&=0 \end {array} \]	✓	✓	✓	✓	0.672
7500	18323	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+y^{2}+2 y y^{\prime } x&=0 \end {array} \]	✓	✓	✓	✓	0.672