ﬁrst order ode separable

Table 2.397: ﬁrst order ode separable


#	ODE	ODE classiﬁcation	Solved?

27	\[ {}y^{\prime } = 2 x^{2} y^{2} \] i.c.	[_separable]	✓

28	\[ {}y^{\prime } = \ln \left (y\right ) x \] i.c.	[_separable]	✓

33	\[ {}y y^{\prime } = x -1 \] i.c.	[_separable]	✓

34	\[ {}y y^{\prime } = x -1 \] i.c.	[_separable]	✓

41	\[ {}y^{\prime }+2 x y = 0 \]	[_separable]	✓

42	\[ {}y^{\prime }+2 x y^{2} = 0 \]	[_separable]	✓

43	\[ {}y^{\prime } = y \sin \left (x \right ) \]	[_separable]	✓

44	\[ {}\left (x +1\right ) y^{\prime } = 4 y \]	[_separable]	✓

45	\[ {}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}} \]	[_separable]	✓

48	\[ {}y^{\prime } = 2 x \sec \left (y\right ) \]	[_separable]	✓

49	\[ {}\left (-x^{2}+1\right ) y^{\prime } = 2 y \]	[_separable]	✓

50	\[ {}\left (x +1\right )^{2} y^{\prime } = \left (1+y\right )^{2} \]	[_separable]	✓

51	\[ {}y^{\prime } = x y^{3} \]	[_separable]	✓

52	\[ {}y y^{\prime } = x \left (1+y^{2}\right ) \]	[_separable]	✓

53	\[ {}y^{3} y^{\prime } = \left (1+y^{4}\right ) \cos \left (x \right ) \]	[_separable]	✓

54	\[ {}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}} \]	[_separable]	✓

55	\[ {}y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \]	[_separable]	✓

56	\[ {}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x \]	[_separable]	✓

57	\[ {}y^{\prime } = 1+x +y+x y \]	[_separable]	✓

58	\[ {}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2} \]	[_separable]	✓

59	\[ {}y^{\prime } = y \,{\mathrm e}^{x} \] i.c.	[_separable]	✓

60	\[ {}y^{\prime } = 3 x^{2} \left (1+y^{2}\right ) \] i.c.	[_separable]	✓

61	\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \] i.c.	[_separable]	✓

62	\[ {}y^{\prime } = 4 x^{3} y-y \] i.c.	[_separable]	✓

64	\[ {}y^{\prime } \tan \left (x \right ) = y \] i.c.	[_separable]	✓

65	\[ {}y^{\prime } x -y = 2 x^{2} y \] i.c.	[_separable]	✓

66	\[ {}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2} \] i.c.	[_separable]	✓

67	\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \] i.c.	[_separable]	✓

68	\[ {}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2} \] i.c.	[_separable]	✓

83	\[ {}y^{\prime } x +y = 3 x y \] i.c.	[_separable]	✓

87	\[ {}y^{\prime }+2 x y = x \] i.c.	[_separable]	✓

88	\[ {}y^{\prime } = \left (1-y\right ) \cos \left (x \right ) \] i.c.	[_separable]	✓

92	\[ {}y^{\prime } = 1+x +y+x y \] i.c.	[_separable]	✓

96	\[ {}\left (x^{2}+4\right ) y^{\prime }+3 x y = x \] i.c.	[_separable]	✓

103	\[ {}y^{\prime }+p \left (x \right ) y = 0 \]	[_separable]	✓

124	\[ {}y^{2} y^{\prime }+2 x y^{3} = 6 x \]	[_separable]	✓

146	\[ {}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0 \]	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓

180	\[ {}x y^{2}+3 y^{2}-x^{2} y^{\prime } = 0 \]	[_separable]	✓

183	\[ {}3 y+x^{4} y^{\prime } = 2 x y \]	[_separable]	✓

184	\[ {}2 x y^{2}+x^{2} y^{\prime } = y^{2} \]	[_separable]	✓

188	\[ {}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2} \]	[_separable]	✓

191	\[ {}4 x y^{2}+y^{\prime } = 5 x^{4} y^{2} \]	[_separable]	✓

197	\[ {}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2} \]	[_separable]	✓

202	\[ {}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2} \]	[_separable]	✓

209	\[ {}y^{\prime } = 3 \left (y+7\right ) x^{2} \]	[_separable]	✓

210	\[ {}y^{\prime } = x y^{3}-x y \]	[_separable]	✓

213	\[ {}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1} \]	[_separable]	✓

214	\[ {}y^{\prime } = \frac {\sqrt {y}-y}{\tan \left (x \right )} \]	[_separable]	✓

669	\[ {}y^{\prime } = 2 x^{2} y^{2} \] i.c.	[_separable]	✓

670	\[ {}y^{\prime } = \ln \left (y\right ) x \]	[_separable]	✓

673	\[ {}y y^{\prime } = x -1 \] i.c.	[_separable]	✓

674	\[ {}y y^{\prime } = x -1 \] i.c.	[_separable]	✓

677	\[ {}y^{\prime }+2 x y = 0 \]	[_separable]	✓

678	\[ {}y^{\prime }+2 x y^{2} = 0 \]	[_separable]	✓

679	\[ {}y^{\prime } = y \sin \left (x \right ) \]	[_separable]	✓

680	\[ {}\left (x +1\right ) y^{\prime } = 4 y \]	[_separable]	✓

681	\[ {}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}} \]	[_separable]	✓

684	\[ {}y^{\prime } = 2 x \sec \left (y\right ) \]	[_separable]	✓

685	\[ {}\left (-x^{2}+1\right ) y^{\prime } = 2 y \]	[_separable]	✓

686	\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (1+y\right )^{2} \]	[_separable]	✓

687	\[ {}y^{\prime } = x y^{3} \]	[_separable]	✓

688	\[ {}y y^{\prime } = x \left (1+y^{2}\right ) \]	[_separable]	✓

689	\[ {}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}} \]	[_separable]	✓

690	\[ {}y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \]	[_separable]	✓

691	\[ {}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x \]	[_separable]	✓

692	\[ {}y^{\prime } = 1+x +y+x y \]	[_separable]	✓

693	\[ {}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2} \]	[_separable]	✓

694	\[ {}y^{\prime } = y \,{\mathrm e}^{x} \] i.c.	[_separable]	✓

695	\[ {}y^{\prime } = 3 x^{2} \left (1+y^{2}\right ) \] i.c.	[_separable]	✓

696	\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \] i.c.	[_separable]	✓

697	\[ {}y^{\prime } = 4 x^{3} y-y \] i.c.	[_separable]	✓

699	\[ {}y^{\prime } \tan \left (x \right ) = y \] i.c.	[_separable]	✓

700	\[ {}y^{\prime } x -y = 2 x^{2} y \] i.c.	[_separable]	✓

701	\[ {}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2} \] i.c.	[_separable]	✓

702	\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \] i.c.	[_separable]	✓

703	\[ {}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2} \] i.c.	[_separable]	✓

714	\[ {}y^{\prime } x +y = 3 x y \] i.c.	[_separable]	✓

718	\[ {}y^{\prime }+2 x y = x \] i.c.	[_separable]	✓

719	\[ {}y^{\prime } = \left (1-y\right ) \cos \left (x \right ) \] i.c.	[_separable]	✓

723	\[ {}y^{\prime } = 1+x +y+x y \] i.c.	[_separable]	✓

727	\[ {}\left (x^{2}+4\right ) y^{\prime }+3 x y = x \] i.c.	[_separable]	✓

748	\[ {}y^{2} y^{\prime }+2 x y^{3} = 6 x \]	[_separable]	✓

770	\[ {}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0 \]	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓

772	\[ {}x y^{2}+3 y^{2}-x^{2} y^{\prime } = 0 \]	[_separable]	✓

775	\[ {}3 y+x^{4} y^{\prime } = 2 x y \]	[_separable]	✓

776	\[ {}2 x y^{2}+x^{2} y^{\prime } = y^{2} \]	[_separable]	✓

780	\[ {}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2} \]	[_separable]	✓

789	\[ {}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2} \]	[_separable]	✓

794	\[ {}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2} \]	[_separable]	✓

800	\[ {}y^{\prime } = 3 \left (y+7\right ) x^{2} \]	[_separable]	✓

801	\[ {}y^{\prime } = 3 \left (y+7\right ) x^{2} \]	[_separable]	✓

802	\[ {}y^{\prime } = x y^{3}-x y \]	[_separable]	✓

805	\[ {}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1} \]	[_separable]	✓

806	\[ {}y^{\prime } = \cot \left (x \right ) \left (\sqrt {y}-y\right ) \]	[_separable]	✓

1129	\[ {}y^{\prime } = \frac {x^{2}}{y} \]	[_separable]	✓

1130	\[ {}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y} \]	[_separable]	✓

1131	\[ {}\sin \left (x \right ) y^{2}+y^{\prime } = 0 \]	[_separable]	✓

1132	\[ {}y^{\prime } = \frac {3 x^{2}-1}{3+2 y} \]	[_separable]	✓

1133	\[ {}y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \]	[_separable]	✓

1134	\[ {}y^{\prime } x = \sqrt {1-y^{2}} \]	[_separable]	✓

1136	\[ {}y^{\prime } = \frac {x^{2}}{1+y^{2}} \]	[_separable]	✓

1137	\[ {}y^{\prime } = \left (-2 x +1\right ) y^{2} \] i.c.	[_separable]	✓

1138	\[ {}y^{\prime } = \frac {-2 x +1}{y} \] i.c.	[_separable]	✓

1139	\[ {}x +y y^{\prime } {\mathrm e}^{-x} = 0 \] i.c.	[_separable]	✓

1140	\[ {}r^{\prime } = \frac {r^{2}}{x} \] i.c.	[_separable]	✓

1141	\[ {}y^{\prime } = \frac {2 x}{y+x^{2} y} \] i.c.	[_separable]	✓

1142	\[ {}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}} \] i.c.	[_separable]	✓

1143	\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] i.c.	[_separable]	✓

1144	\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}} \] i.c.	[_separable]	✓

1145	\[ {}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \] i.c.	[_separable]	✓

1146	\[ {}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \] i.c.	[_separable]	✓

1147	\[ {}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

1148	\[ {}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right ) \] i.c.	[_separable]	✓

1149	\[ {}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}} \] i.c.	[_separable]	✓

1150	\[ {}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}} \] i.c.	[_separable]	✓

1151	\[ {}y^{\prime } = 2 y^{2}+x y^{2} \] i.c.	[_separable]	✓

1152	\[ {}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y} \] i.c.	[_separable]	✓

1153	\[ {}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y} \] i.c.	[_separable]	✓

1154	\[ {}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right ) \] i.c.	[_separable]	✓

1155	\[ {}y^{\prime } = \frac {t \left (4-y\right ) y}{3} \]	[_separable]	✓

1156	\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{1+t} \]	[_separable]	✓

1167	\[ {}y+\left (t -4\right ) t y^{\prime } = 0 \] i.c.	[_separable]	✓

1172	\[ {}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \]	[_separable]	✓

1173	\[ {}y^{\prime } = \frac {\cot \left (t \right ) y}{1+y} \]	[_separable]	✓

1174	\[ {}y^{\prime } = -\frac {4 t}{y} \]	[_separable]	✓

1175	\[ {}y^{\prime } = 2 t y^{2} \]	[_separable]	✓

1177	\[ {}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y} \]	[_separable]	✓

1178	\[ {}y^{\prime } = t \left (3-y\right ) y \]	[_separable]	✓

1193	\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \]	[_separable]	✓

1196	\[ {}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

1204	\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]	[_separable]	✓

1207	\[ {}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0 \]	[_separable]	✓

1209	\[ {}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

1219	\[ {}y^{\prime } = \frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \]	[_separable]	✓

1221	\[ {}y^{\prime } = 3-6 x +y-2 x y \]	[_separable]	✓

1224	\[ {}y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )} \]	[_separable]	✓

1227	\[ {}\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y} = 0 \]	[_separable]	✓

1230	\[ {}y^{\prime } = 1+2 x +y^{2}+2 x y^{2} \]	[_separable]	✓

1232	\[ {}\left ({\mathrm e}^{x}+1\right ) y^{\prime } = y-y \,{\mathrm e}^{x} \]	[_separable]	✓

1237	\[ {}y^{\prime } = {\mathrm e}^{x +y} \]	[_separable]	✓

1239	\[ {}y^{\prime } = \frac {x^{2}-1}{1+y^{2}} \] i.c.	[_separable]	✓

1241	\[ {}2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime } = 0 \]	[_separable]	✓

1521	\[ {}y^{\prime }+2 x y = x \]	[_separable]	✓

1522	\[ {}2 y^{\prime }+x \left (-1+y^{2}\right ) = 0 \]	[_separable]	✓

1523	\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \]	[_separable]	✓

1532	\[ {}y^{\prime } = x \left (1+y^{2}\right ) \] i.c.	[_separable]	✓

1533	\[ {}y^{\prime } = -\frac {y \left (1+y\right )}{x} \] i.c.	[_separable]	✓

1538	\[ {}y^{\prime }+3 x^{2} y = 0 \]	[_separable]	✓

1539	\[ {}y^{\prime } x +y \ln \left (x \right ) = 0 \]	[_separable]	✓

1540	\[ {}y^{\prime } x +3 y = 0 \]	[_separable]	✓

1541	\[ {}x^{2} y^{\prime }+y = 0 \]	[_separable]	✓

1542	\[ {}y^{\prime }+\frac {\left (x +1\right ) y}{x} = 0 \] i.c.	[_separable]	✓

1543	\[ {}y^{\prime } x +\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0 \] i.c.	[_separable]	✓

1544	\[ {}y^{\prime } x +\left (1+x \cot \left (x \right )\right ) y = 0 \] i.c.	[_separable]	✓

1545	\[ {}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0 \] i.c.	[_separable]	✓

1546	\[ {}y^{\prime }+\frac {k y}{x} = 0 \] i.c.	[_separable]	✓

1547	\[ {}y^{\prime }+\tan \left (k x \right ) y = 0 \] i.c.	[_separable]	✓

1569	\[ {}y^{\prime }+2 x y = x \] i.c.	[_separable]	✓

1573	\[ {}y^{\prime } x -2 y = -1 \] i.c.	[_separable]	✓

1578	\[ {}y^{\prime } = \frac {3 x^{2}+2 x +1}{-2+y} \]	[_separable]	✓

1579	\[ {}\sin \left (x \right ) \sin \left (y\right )+y^{\prime } \cos \left (y\right ) = 0 \]	[_separable]	✓

1580	\[ {}y^{\prime } x +y^{2}+y = 0 \]	[_separable]	✓

1581	\[ {}\left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1} = 0 \]	[_separable]	✓

1582	\[ {}x^{2} y y^{\prime } = \left (-1+y^{2}\right )^{{3}/{2}} \]	[_separable]	✓

1583	\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \]	[_separable]	✓

1584	\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = 0 \]	[_separable]	✓

1585	\[ {}y^{\prime } = \left (x -1\right ) \left (-1+y\right ) \left (-2+y\right ) \]	[_separable]	✓

1586	\[ {}\left (-1+y\right )^{2} y^{\prime } = 2 x +3 \]	[_separable]	✓

1587	\[ {}y^{\prime } = \frac {x^{2}+3 x +2}{-2+y} \] i.c.	[_separable]	✓

1588	\[ {}y^{\prime }+x \left (y^{2}+y\right ) = 0 \] i.c.	[_separable]	✓

1589	\[ {}\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right ) = 0 \] i.c.	[_separable]	✓

1590	\[ {}y^{\prime }+\frac {\left (1+y\right ) \left (-1+y\right ) \left (-2+y\right )}{x +1} = 0 \] i.c.	[_separable]	✓

1591	\[ {}y^{\prime }+2 x \left (1+y\right ) = 0 \] i.c.	[_separable]	✓

1592	\[ {}y^{\prime } = 2 x y \left (1+y^{2}\right ) \] i.c.	[_separable]	✓

1593	\[ {}\left (x^{2}+2\right ) y^{\prime } = 4 x \left (y^{2}+2 y+1\right ) \]	[_separable]	✓

1594	\[ {}y^{\prime } = -2 x \left (y^{3}-3 y+2\right ) \] i.c.	[_separable]	✓

1595	\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] i.c.	[_separable]	✓

1597	\[ {}y y^{\prime }+x = 0 \] i.c.	[_separable]	✓

1598	\[ {}y^{\prime }+x^{2} \left (1+y\right ) \left (-2+y\right )^{2} = 0 \]	[_separable]	✓

1599	\[ {}\left (x +1\right ) \left (x -2\right ) y^{\prime }+y = 0 \] i.c.	[_separable]	✓

1600	\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \]	[_separable]	✓

1601	\[ {}y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0 \]	[_separable]	✓

1602	\[ {}y^{\prime } = \frac {\cos \left (x \right )}{\sin \left (y\right )} \] i.c.	[_separable]	✓

1613	\[ {}y^{\prime } = 2 x y \]	[_separable]	✓

1617	\[ {}y^{\prime } = x \left (-1+y^{2}\right )^{{2}/{3}} \]	[_separable]	✓

1620	\[ {}y^{\prime } = \frac {\tan \left (y\right )}{x -1} \]	[_separable]	✓

1622	\[ {}y^{\prime } = 3 x \left (-1+y\right )^{{1}/{3}} \] i.c.	[_separable]	✓

1623	\[ {}y^{\prime } = 3 x \left (-1+y\right )^{{1}/{3}} \] i.c.	[_separable]	✓

1624	\[ {}y^{\prime } = 3 x \left (-1+y\right )^{{1}/{3}} \] i.c.	[_separable]	✓

1636	\[ {}y^{\prime }-x y = x y^{{3}/{2}} \] i.c.	[_separable]	✓

1680	\[ {}6 x^{2} y^{2}+4 x^{3} y y^{\prime } = 0 \]	[_separable]	✓

1690	\[ {}\frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime } = 0 \]	[_separable]	✓

1692	\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]	[_separable]	✓

1699	\[ {}\left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left ({\mathrm e}^{x}+1\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

1701	\[ {}\left (2 x -1\right ) \left (-1+y\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

1712	\[ {}-y^{2}+x^{2} y^{\prime } = 0 \]	[_separable]	✓

1713	\[ {}y-y^{\prime } x = 0 \]	[_separable]	✓

1714	\[ {}3 x^{2} y+2 x^{3} y^{\prime } = 0 \]	[_separable]	✓

1722	\[ {}x^{2} y+4 x y+2 y+\left (x^{2}+x \right ) y^{\prime } = 0 \]	[_separable]	✓


1723	\[ {}-y+\left (x^{4}-x \right ) y^{\prime } = 0 \]	[_separable]	✓

1726	\[ {}y \sin \left (y\right )+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime } = 0 \]	[_separable]	✓

1727	\[ {}a y+b x y+\left (c x +d x y\right ) y^{\prime } = 0 \]	[_separable]	✓

1729	\[ {}2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime } = 0 \]	[_separable]	✓

1731	\[ {}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0 \]	[_separable]	✓

1732	\[ {}y \left (x \cos \left (x \right )+2 \sin \left (x \right )\right )+x \left (1+y\right ) y^{\prime } = 0 \]	[_separable]	✓

2299	\[ {}\cos \left (t \right ) y+y^{\prime } = 0 \]	[_separable]	✓

2300	\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \]	[_separable]	✓

2304	\[ {}t^{2} y+y^{\prime } = t^{2} \]	[_separable]	✓

2306	\[ {}\sqrt {t^{2}+1}\, y+y^{\prime } = 0 \] i.c.	[_separable]	✓

2307	\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \]	[_separable]	✓

2308	\[ {}y^{\prime }-2 t y = t \] i.c.	[_separable]	✓

2313	\[ {}4 t y+\left (t^{2}+1\right ) y^{\prime } = t \] i.c.	[_separable]	✓

2318	\[ {}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2} \]	[_separable]	✓

2319	\[ {}y^{\prime } = \left (1+t \right ) \left (1+y\right ) \]	[_separable]	✓

2320	\[ {}y^{\prime } = 1-t +y^{2}-t y^{2} \]	[_separable]	✓

2321	\[ {}y^{\prime } = {\mathrm e}^{3+t +y} \]	[_separable]	✓

2322	\[ {}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right ) \]	[_separable]	✓

2323	\[ {}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0 \] i.c.	[_separable]	✓

2324	\[ {}y^{\prime } = \frac {2 t}{y+t^{2} y} \] i.c.	[_separable]	✓

2325	\[ {}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}} \] i.c.	[_separable]	✓

2326	\[ {}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y} \] i.c.	[_separable]	✓

2327	\[ {}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1} \] i.c.	[_separable]	✓

2329	\[ {}3 y^{\prime } t = \cos \left (t \right ) y \] i.c.	[_separable]	✓

2342	\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \] i.c.	[_separable]	✓

2360	\[ {}y^{\prime } = t \left (1+y\right ) \] i.c.	[_separable]	✓

2361	\[ {}y^{\prime } = t \sqrt {1-y^{2}} \] i.c.	[_separable]	✓

2472	\[ {}\cos \left (t \right ) y+y^{\prime } = 0 \]	[_separable]	✓

2473	\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \]	[_separable]	✓

2477	\[ {}t^{2} y+y^{\prime } = t^{2} \]	[_separable]	✓

2479	\[ {}\sqrt {t^{2}+1}\, y+y^{\prime } = 0 \] i.c.	[_separable]	✓

2480	\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \] i.c.	[_separable]	✓

2481	\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \] i.c.	[_separable]	✓

2482	\[ {}y^{\prime }-2 t y = t \] i.c.	[_separable]	✓

2487	\[ {}4 t y+\left (t^{2}+1\right ) y^{\prime } = t \] i.c.	[_separable]	✓

2489	\[ {}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2} \]	[_separable]	✓

2490	\[ {}y^{\prime } = \left (1+t \right ) \left (1+y\right ) \]	[_separable]	✓

2491	\[ {}y^{\prime } = 1-t +y^{2}-t y^{2} \]	[_separable]	✓

2492	\[ {}y^{\prime } = {\mathrm e}^{3+t +y} \]	[_separable]	✓

2493	\[ {}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right ) \]	[_separable]	✓

2494	\[ {}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0 \] i.c.	[_separable]	✓

2495	\[ {}y^{\prime } = \frac {2 t}{y+t^{2} y} \] i.c.	[_separable]	✓

2496	\[ {}\sqrt {1+y^{2}}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}} \] i.c.	[_separable]	✓

2497	\[ {}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y} \] i.c.	[_separable]	✓

2498	\[ {}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1} \] i.c.	[_separable]	✓

2500	\[ {}3 y^{\prime } t = \cos \left (t \right ) y \] i.c.	[_separable]	✓

2514	\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \] i.c.	[_separable]	✓

2519	\[ {}y^{\prime } = 2 t \left (1+y\right ) \] i.c.	[_separable]	✓

2535	\[ {}y^{\prime } = t \left (1+y\right ) \] i.c.	[_separable]	✓

2536	\[ {}y^{\prime } = t y^{a} \] i.c.	[_separable]	✓

2537	\[ {}y^{\prime } = t \sqrt {1-y^{2}} \] i.c.	[_separable]	✓

2841	\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = 0 \]	[_separable]	✓

2842	\[ {}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

2843	\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]	[_separable]	✓

2844	\[ {}y^{\prime } x +y = 0 \]	[_separable]	✓

2845	\[ {}y^{\prime } = 2 x y \]	[_separable]	✓

2846	\[ {}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0 \]	[_separable]	✓

2847	\[ {}\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime } = 0 \]	[_separable]	✓

2848	\[ {}\left (x +1\right ) y^{\prime }-1+y = 0 \]	[_separable]	✓

2849	\[ {}y^{\prime } \tan \left (x \right )-y = 1 \]	[_separable]	✓

2850	\[ {}y+3+\cot \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

2851	\[ {}y^{\prime } = \frac {x}{y} \]	[_separable]	✓

2853	\[ {}y^{\prime } x +y = y^{2} \]	[_separable]	✓

2854	\[ {}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0 \]	[_separable]	✓

2855	\[ {}\sec \left (x \right ) \cos \left (y\right )^{2} = \cos \left (x \right ) \sin \left (y\right ) y^{\prime } \]	[_separable]	✓

2856	\[ {}y^{\prime } x +y = x y \left (y^{\prime }-1\right ) \]	[_separable]	✓

2857	\[ {}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0 \]	[_separable]	✓

2858	\[ {}y = x y+x^{2} y^{\prime } \]	[_separable]	✓

2859	\[ {}\tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

2860	\[ {}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0 \]	[_separable]	✓

2861	\[ {}y^{\prime } = \frac {y}{x} \] i.c.	[_separable]	✓

2862	\[ {}y^{\prime } x +2 y = 0 \] i.c.	[_separable]	✓

2863	\[ {}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

2864	\[ {}x^{2} y^{\prime }+y^{2} = 0 \] i.c.	[_separable]	✓

2867	\[ {}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (x -1\right )} \] i.c.	[_separable]	✓

2869	\[ {}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5 \] i.c.	[_separable]	✓

2870	\[ {}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2 \] i.c.	[_separable]	✓

2925	\[ {}\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime } = 0 \]	[_separable]	✓

2939	\[ {}\left (x -2 x y\right ) y^{\prime }+2 y = 0 \]	[_separable]	✓

2953	\[ {}\left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

2991	\[ {}y^{\prime }-x y = \frac {x}{y} \]	[_separable]	✓

2993	\[ {}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0 \]	[_separable]	✓

2996	\[ {}y^{\prime } \cos \left (y\right )+\left (\sin \left (y\right )-1\right ) \cos \left (x \right ) = 0 \]	[_separable]	✓

3004	\[ {}\left (1-x \right ) y^{\prime }-1-y = 0 \]	[_separable]	✓

3011	\[ {}6+2 y = x y^{\prime } y \]	[_separable]	✓

3015	\[ {}y-y^{\prime } x = 2 y^{\prime }+2 y^{2} \]	[_separable]	✓

3016	\[ {}\tan \left (y\right ) = \left (3 x +4\right ) y^{\prime } \]	[_separable]	✓

3020	\[ {}r^{\prime } = r \cot \left (\theta \right ) \]	[_separable]	✓

3024	\[ {}y^{\prime } = \cos \left (y\right ) \cos \left (x \right )^{2} \]	[_separable]	✓

3028	\[ {}3 x -6 = x y^{\prime } y \]	[_separable]	✓

3031	\[ {}y^{\prime } x +y \left (1+y^{2}\right ) = 0 \]	[_separable]	✓

3033	\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right ) = \left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } \]	[_separable]	✓

3040	\[ {}x \sqrt {1-y}-y^{\prime } \sqrt {-x^{2}+1} = 0 \] i.c.	[_separable]	✓

3042	\[ {}x \,{\mathrm e}^{-y^{2}}+y y^{\prime } = 0 \] i.c.	[_separable]	✓

3052	\[ {}4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

3057	\[ {}2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y \] i.c.	[_separable]	✓

3293	\[ {}{y^{\prime }}^{3}+\left (x +y-2 x y\right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right ) = 0 \]	[_quadrature]	✓

3334	\[ {}y^{2}-2 x y^{\prime } y+{y^{\prime }}^{2} \left (x^{2}-1\right ) = 0 \]	[_separable]	✓

3409	\[ {}y^{\prime } = x y \]	[_separable]	✓

3410	\[ {}y^{\prime } = x^{2} y^{2} \]	[_separable]	✓

3411	\[ {}y^{\prime } = -x \,{\mathrm e}^{y} \]	[_separable]	✓

3412	\[ {}y^{\prime } \sin \left (y\right ) = x^{2} \]	[_separable]	✓

3413	\[ {}y^{\prime } x = \sqrt {1-y^{2}} \]	[_separable]	✓

3427	\[ {}y^{\prime } = \frac {{\mathrm e}^{t}}{y} \] i.c.	[_separable]	✓

3431	\[ {}y^{\prime } = \frac {y}{t} \]	[_separable]	✓

3432	\[ {}y^{\prime } = -\frac {t}{y} \]	[_separable]	✓

3438	\[ {}y^{\prime } = \left (t^{2}+1\right ) y \]	[_separable]	✓

3451	\[ {}y^{\prime } = \frac {2 y}{1+t} \] i.c.	[_separable]	✓

3453	\[ {}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right ) \] i.c.	[_separable]	✓

3457	\[ {}y^{\prime }-x y^{3} = 0 \]	[_separable]	✓

3458	\[ {}\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1} = 0 \]	[_separable]	✓

3459	\[ {}x^{2} y^{\prime }+x y^{2} = 4 y^{2} \]	[_separable]	✓

3470	\[ {}y^{\prime } = \tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \]	[_separable]	✓

3473	\[ {}y^{\prime } = \frac {4 y^{2}}{x^{2}}-y^{2} \]	[_separable]	✓

3515	\[ {}y^{\prime } = 2 x y \]	[_separable]	✓

3516	\[ {}y^{\prime } = \frac {y^{2}}{x^{2}+1} \]	[_separable]	✓

3517	\[ {}{\mathrm e}^{x +y} y^{\prime }-1 = 0 \]	[_separable]	✓

3518	\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \]	[_separable]	✓

3519	\[ {}y-\left (x -2\right ) y^{\prime } = 0 \]	[_separable]	✓

3520	\[ {}y^{\prime } = \frac {2 x \left (-1+y\right )}{x^{2}+3} \]	[_separable]	✓

3521	\[ {}y-y^{\prime } x = 3-2 x^{2} y^{\prime } \]	[_separable]	✓

3522	\[ {}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \]	[_separable]	✓

3523	\[ {}y^{\prime } = \frac {x \left (-1+y^{2}\right )}{2 \left (x -2\right ) \left (x -1\right )} \]	[_separable]	✓

3525	\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0 \]	[_separable]	✓

3526	\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \] i.c.	[_separable]	✓

3527	\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = a x \] i.c.	[_separable]	✓

3528	\[ {}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )} \] i.c.	[_separable]	✓

3529	\[ {}y^{\prime } = y^{3} \sin \left (x \right ) \]	[_separable]	✓

3562	\[ {}y^{\prime } = \frac {y}{2 x} \]	[_separable]	✓

3593	\[ {}y^{\prime } = 2 x y \]	[_separable]	✓

3594	\[ {}y^{\prime } = \frac {y^{2}}{x^{2}+1} \]	[_separable]	✓

3595	\[ {}{\mathrm e}^{x +y} y^{\prime }-1 = 0 \]	[_separable]	✓

3596	\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \]	[_separable]	✓

3597	\[ {}y-\left (x -1\right ) y^{\prime } = 0 \]	[_separable]	✓

3598	\[ {}y^{\prime } = \frac {2 x \left (-1+y\right )}{x^{2}+3} \]	[_separable]	✓

3599	\[ {}y-y^{\prime } x = 3-2 x^{2} y^{\prime } \]	[_separable]	✓

3600	\[ {}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \]	[_separable]	✓

3601	\[ {}y^{\prime } = \frac {x \left (-1+y^{2}\right )}{2 \left (x -2\right ) \left (x -1\right )} \]	[_separable]	✓

3602	\[ {}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+2 \]	[_separable]	✓

3603	\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0 \]	[_separable]	✓

3604	\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \] i.c.	[_separable]	✓

3605	\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = a x \] i.c.	[_separable]	✓

3606	\[ {}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )} \] i.c.	[_separable]	✓

3607	\[ {}y^{\prime } = y^{3} \sin \left (x \right ) \] i.c.	[_separable]	✓

3642	\[ {}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0 \]	[_separable]	✓

3669	\[ {}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right ) \]	[_separable]	✓

3683	\[ {}\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {x +1}} = \frac {1}{2 \sqrt {x +1}} \]	[_separable]	✓

4094	\[ {}x^{2}+x -1+\left (2 x y+y\right ) y^{\prime } = 0 \]	[_separable]	✓

4095	\[ {}{\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime } = 0 \]	[_separable]	✓

4096	\[ {}\left (x +1\right ) y^{\prime }-x^{2} y^{2} = 0 \]	[_separable]	✓

4102	\[ {}y^{\prime } = {\mathrm e}^{x -2 y} \] i.c.	[_separable]	✓

4105	\[ {}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

4110	\[ {}2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right ) = 0 \] i.c.	[_separable]	✓

4111	\[ {}x y^{\prime } y = \left (x +1\right ) \left (1+y\right ) \] i.c.	[_separable]	✓

4190	\[ {}y y^{\prime } = x \]	[_separable]	✓

4213	\[ {}3 y^{2} y^{\prime } = 2 x -1 \]	[_separable]	✓

4214	\[ {}y^{\prime } = 6 x y^{2} \]	[_separable]	✓

4215	\[ {}y^{\prime } = {\mathrm e}^{y} \sin \left (x \right ) \]	[_separable]	✓

4216	\[ {}y^{\prime } = {\mathrm e}^{x -y} \]	[_separable]	✓

4217	\[ {}y^{\prime } = x \sec \left (y\right ) \]	[_separable]	✓

4219	\[ {}y^{\prime } x = y \]	[_separable]	✓

4220	\[ {}\left (1-x \right ) y^{\prime } = y \]	[_separable]	✓

4221	\[ {}y^{\prime } = \frac {4 x y}{x^{2}+1} \]	[_separable]	✓

4222	\[ {}y^{\prime } = \frac {2 y}{x^{2}-1} \]	[_separable]	✓

4223	\[ {}-y^{2}+x^{2} y^{\prime } = 0 \] i.c.	[_separable]	✓

4224	\[ {}y^{\prime }+2 x y = 0 \] i.c.	[_separable]	✓

4225	\[ {}\cot \left (x \right ) y^{\prime } = y \] i.c.	[_separable]	✓

4226	\[ {}y^{\prime } = x \,{\mathrm e}^{-2 y} \] i.c.	[_separable]	✓

4227	\[ {}y^{\prime }-2 x y = 2 x \] i.c.	[_separable]	✓

4228	\[ {}y^{\prime } x = x y+y \] i.c.	[_separable]	✓

4230	\[ {}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right ) \] i.c.	[_separable]	✓

4231	\[ {}y^{\prime } x = 2 y \left (-1+y\right ) \] i.c.	[_separable]	✓

4232	\[ {}2 y^{\prime } x = 1-y^{2} \] i.c.	[_separable]	✓

4233	\[ {}\left (1-x \right ) y^{\prime } = x y \]	[_separable]	✓

4234	\[ {}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y \]	[_separable]	✓

4235	\[ {}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right ) \]	[_separable]	✓

4236	\[ {}{\mathrm e}^{y} y^{\prime }+2 x = 2 x \,{\mathrm e}^{y} \]	[_separable]	✓

4237	\[ {}y \,{\mathrm e}^{2 x} y^{\prime }+2 x = 0 \] i.c.	[_separable]	✓

4238	\[ {}x y^{\prime } y = \sqrt {y^{2}-9} \] i.c.	[_separable]	✓

4254	\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]	[_separable]	✓

4255	\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

4257	\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \]	[_separable]	✓

4258	\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \]	[_separable]	✓

4265	\[ {}y-\left (x +x y^{3}\right ) y^{\prime } = 0 \]	[_separable]	✓

4295	\[ {}x^{2} y^{\prime }+2 x y = 0 \]	[_separable]	✓

4301	\[ {}x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right ) = 0 \]	[_separable]	✓

4302	\[ {}x \left (x -1\right ) y^{\prime } = \cot \left (y\right ) \]	[_separable]	✓

4303	\[ {}r y^{\prime } = \frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \]	[_separable]	✓

4304	\[ {}\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}} = 0 \]	[_separable]	✓

4305	\[ {}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \] i.c.	[_separable]	✓

4307	\[ {}\cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

4309	\[ {}x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

4310	\[ {}x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime } = 0 \]	[_separable]	✓

4311	\[ {}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0 \]	[_separable]	✓

4312	\[ {}x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

4313	\[ {}x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime } = 0 \]	[_separable]	✓

4361	\[ {}1-\left (y-2 x y\right ) y^{\prime } = 0 \]	[_separable]	✓

4398	\[ {}y^{\prime } = \frac {y+2}{x +1} \]	[_separable]	✓

4412	\[ {}x y+2 x^{3} y+x^{2} y^{\prime } = 0 \]	[_separable]	✓

4429	\[ {}y \ln \left (x \right ) \ln \left (y\right )+y^{\prime } = 0 \]	[_separable]	✓

4618	\[ {}y^{\prime } = a \,x^{n} y \]	[_separable]	✓

4621	\[ {}y^{\prime } = \cot \left (x \right ) y \]	[_separable]	✓

4624	\[ {}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \]	[_separable]	✓

4632	\[ {}y^{\prime } = y \sec \left (x \right ) \]	[_separable]	✓

4634	\[ {}y^{\prime } = y \tan \left (x \right ) \]	[_separable]	✓

4643	\[ {}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \]	[_separable]	✓

4671	\[ {}y^{\prime } = x y \left (3+y\right ) \]	[_separable]	✓

4675	\[ {}y^{\prime } = a x y^{2} \]	[_separable]	✓

4676	\[ {}y^{\prime } = x^{n} \left (a +b y^{2}\right ) \]	[_separable]	✓

4682	\[ {}y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right ) = 0 \]	[_separable]	✓

4684	\[ {}y^{\prime } = \left (a +b y+c y^{2}\right ) f \left (x \right ) \]	[_separable]	✓

4690	\[ {}y^{\prime } = x y^{3} \]	[_separable]	✓

4695	\[ {}y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right ) = 0 \]	[_separable]	✓

4709	\[ {}y^{\prime } = \cos \left (y\right ) \cos \left (x \right )^{2} \]	[_separable]	✓

4710	\[ {}y^{\prime } = \sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \]	[_separable]	✓

4715	\[ {}y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2} = 0 \]	[_separable]	✓

4716	\[ {}y^{\prime } = \cot \left (x \right ) \cot \left (y\right ) \]	[_separable]	✓

4717	\[ {}y^{\prime }+\cot \left (x \right ) \cot \left (y\right ) = 0 \]	[_separable]	✓

4718	\[ {}y^{\prime } = \sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \]	[_separable]	✓

4719	\[ {}y^{\prime } = \tan \left (x \right ) \cot \left (y\right ) \]	[_separable]	✓

4720	\[ {}y^{\prime }+\tan \left (x \right ) \cot \left (y\right ) = 0 \]	[_separable]	✓

4721	\[ {}y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right ) = 0 \]	[_separable]	✓

4723	\[ {}y^{\prime } = \cos \left (x \right ) \sec \left (y\right )^{2} \]	[_separable]	✓

4724	\[ {}y^{\prime } = \sec \left (x \right )^{2} \sec \left (y\right )^{3} \]	[_separable]	✓

4727	\[ {}y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right ) = 0 \]	[_separable]	✓

4731	\[ {}y^{\prime } = {\mathrm e}^{x +y} \]	[_separable]	✓

4732	\[ {}y^{\prime } = {\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \]	[_separable]	✓

4733	\[ {}y \ln \left (x \right ) \ln \left (y\right )+y^{\prime } = 0 \]	[_separable]	✓

4737	\[ {}y^{\prime } = f \left (x \right ) g \left (y\right ) \]	[_separable]	✓

4752	\[ {}y^{\prime } x = a y \]	[_separable]	✓

4759	\[ {}y^{\prime } x +\left (b x +a \right ) y = 0 \]	[_separable]	✓

4766	\[ {}y^{\prime } x = a +b y^{2} \]	[_separable]	✓

4787	\[ {}y^{\prime } x = y \left (1+y^{2}\right ) \]	[_separable]	✓

4792	\[ {}y^{\prime } x = 4 y-4 \sqrt {y} \]	[_separable]	✓

4793	\[ {}y^{\prime } x +2 y = \sqrt {1+y^{2}} \]	[_separable]	✓

4802	\[ {}y^{\prime } x = \left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \]	[_separable]	✓

4803	\[ {}y^{\prime } x = y-\cot \left (y\right )^{2} \]	[_separable]	✓

4809	\[ {}y^{\prime } x +\tan \left (y\right ) = 0 \]	[_separable]	✓

4815	\[ {}y^{\prime } x = y \ln \left (y\right ) \]	[_separable]	✓

4832	\[ {}\left (x +a \right ) y^{\prime } = b +c y \]	[_separable]	✓

4834	\[ {}\left (x +a \right ) y^{\prime } = y \left (1-a y\right ) \]	[_separable]	✓

4838	\[ {}2 y^{\prime } x = y \left (1+y^{2}\right ) \]	[_separable]	✓

4839	\[ {}2 y^{\prime } x +y \left (1+y^{2}\right ) = 0 \]	[_separable]	✓

4841	\[ {}2 y^{\prime } x +4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0 \]	[_separable]	✓

4843	\[ {}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2 \]	[_separable]	✓

4849	\[ {}x^{2} y^{\prime } = -y+a \]	[_separable]	✓

4854	\[ {}x^{2} y^{\prime } = \left (b x +a \right ) y \]	[_separable]	✓

4859	\[ {}x^{2} y^{\prime } = a +b y^{2} \]	[_separable]	✓

4883	\[ {}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0 \]	[_separable]	✓

4888	\[ {}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0 \]	[_separable]	✓

4894	\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y \]	[_separable]	✓

4895	\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \]	[_separable]	✓

4896	\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2} \]	[_separable]	✓

4899	\[ {}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0 \]	[_separable]	✓

4900	\[ {}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right ) \]	[_separable]	✓

4906	\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \]	[_separable]	✓

4909	\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0 \]	[_separable]	✓

4913	\[ {}x \left (x +1\right ) y^{\prime } = \left (-2 x +1\right ) y \]	[_separable]	✓

4919	\[ {}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y \]	[_separable]	✓

4920	\[ {}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right ) \]	[_separable]	✓

4922	\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0 \]	[_separable]	✓

4924	\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2} \]	[_separable]	✓

4925	\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0 \]	[_separable]	✓

4927	\[ {}2 x^{2} y^{\prime } = y \]	[_separable]	✓

4939	\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \]	[_separable]	✓

4940	\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = c x y \ln \left (y\right ) \]	[_separable]	✓

4941	\[ {}x \left (a x +1\right ) y^{\prime }+a -y = 0 \]	[_separable]	✓

4948	\[ {}x^{3} y^{\prime } = \left (x +1\right ) y^{2} \]	[_separable]	✓

4957	\[ {}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y \]	[_separable]	✓

4958	\[ {}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y \]	[_separable]	✓

4972	\[ {}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right ) \]	[_separable]	✓

4976	\[ {}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y \]	[_separable]	✓

4988	\[ {}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2} \]	[_separable]	✓

4989	\[ {}\left (x -\sqrt {x^{2}+1}\right ) y^{\prime } = y+\sqrt {1+y^{2}} \]	[_separable]	✓

4991	\[ {}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}} \]	[_separable]	✓

4992	\[ {}y^{\prime } \sqrt {b^{2}-x^{2}} = \sqrt {a^{2}-y^{2}} \]	[_separable]	✓

4993	\[ {}x y^{\prime } \sqrt {a^{2}+x^{2}} = y \sqrt {b^{2}+y^{2}} \]	[_separable]	✓

4994	\[ {}x y^{\prime } \sqrt {-a^{2}+x^{2}} = y \sqrt {y^{2}-b^{2}} \]	[_separable]	✓

4998	\[ {}y^{\prime } \sqrt {x^{3}+1} = \sqrt {y^{3}+1} \]	[_separable]	✓

4999	\[ {}y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )} = \sqrt {y \left (1-y\right ) \left (1-a y\right )} \]	[_separable]	✓

5000	\[ {}y^{\prime } \sqrt {-x^{4}+1} = \sqrt {1-y^{4}} \]	[_separable]	✓

5001	\[ {}y^{\prime } \sqrt {x^{4}+x^{2}+1} = \sqrt {1+y^{2}+y^{4}} \]	[_separable]	✓

5005	\[ {}y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (y^{3}+1\right )^{{2}/{3}} = 0 \]	[_separable]	✓

5006	\[ {}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{{2}/{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{{2}/{3}} = 0 \]	[_separable]	✓

5009	\[ {}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \]	[_separable]	✓

5010	\[ {}\left (1-\sin \left (x \right )\right ) y^{\prime }+\cos \left (x \right ) y = 0 \]	[_separable]	✓

5011	\[ {}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0 \]	[_separable]	✓

5015	\[ {}y y^{\prime }+x = 0 \]	[_separable]	✓

5016	\[ {}y y^{\prime }+x \,{\mathrm e}^{x^{2}} = 0 \]	[_separable]	✓

5019	\[ {}y y^{\prime }+x \,{\mathrm e}^{-x} \left (1+y\right ) = 0 \]	[_separable]	✓

5025	\[ {}y y^{\prime } = a x +b x y^{2} \]	[_separable]	✓

5031	\[ {}\left (1+y\right ) y^{\prime } = x^{2} \left (1-y\right ) \]	[_separable]	✓

5074	\[ {}3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2} = 0 \]	[_separable]	✓

5075	\[ {}3 \left (2-y\right ) y^{\prime }+x y = 0 \]	[_separable]	✓

5101	\[ {}x y^{\prime } y+1+y^{2} = 0 \]	[_separable]	✓

5108	\[ {}x y^{\prime } y = a +b y^{2} \]	[_separable]	✓

5110	\[ {}x y^{\prime } y = \left (x^{2}+1\right ) \left (1-y^{2}\right ) \]	[_separable]	✓

5114	\[ {}x \left (1+y\right ) y^{\prime }-\left (1-x \right ) y = 0 \]	[_separable]	✓

5115	\[ {}x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y = 0 \]	[_separable]	✓

5116	\[ {}x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0 \]	[_separable]	✓

5121	\[ {}x \left (a +y\right ) y^{\prime } = y \left (B x +A \right ) \]	[_separable]	✓

5133	\[ {}y \left (1-x \right ) y^{\prime }+x \left (1-y\right ) = 0 \]	[_separable]	✓

5134	\[ {}\left (x +a \right ) \left (x +b \right ) y^{\prime } = x y \]	[_separable]	✓

5136	\[ {}2 x y^{\prime } y+a +y^{2} = 0 \]	[_separable]	✓

5156	\[ {}x \left (a +b y\right ) y^{\prime } = c y \]	[_separable]	✓

5165	\[ {}x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0 \]	[_separable]	✓

5166	\[ {}x^{2} \left (1-y\right ) y^{\prime }+\left (x +1\right ) y^{2} = 0 \]	[_separable]	✓

5167	\[ {}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0 \]	[_separable]	✓

5174	\[ {}2 \left (x +1\right ) x y y^{\prime } = 1+y^{2} \]	[_separable]	✓

5182	\[ {}x y \left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \]	[_separable]	✓

5185	\[ {}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0 \]	[_separable]	✓

5186	\[ {}\left (1+y\right ) y^{\prime } \sqrt {x^{2}+1} = y^{3} \]	[_separable]	✓

5188	\[ {}y^{2} y^{\prime }+x \left (2-y\right ) = 0 \]	[_separable]	✓

5189	\[ {}y^{2} y^{\prime } = x \left (1+y^{2}\right ) \]	[_separable]	✓

5203	\[ {}y \left (1+y\right ) y^{\prime } = x \left (x +1\right ) \]	[_separable]	✓

5229	\[ {}x \left (1-y^{2}\right ) y^{\prime } = \left (x^{2}+1\right ) y \]	[_separable]	✓

5236	\[ {}x \left (a +y\right )^{2} y^{\prime } = b y^{2} \]	[_separable]	✓

5253	\[ {}x^{2} y^{2} y^{\prime }+1-x +x^{3} = 0 \]	[_separable]	✓

5258	\[ {}x^{2} \left (a +y\right )^{2} y^{\prime } = \left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \]	[_separable]	✓

5259	\[ {}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right ) = 0 \]	[_separable]	✓

5260	\[ {}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2} = 0 \]	[_separable]	✓

5263	\[ {}x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y = 0 \]	[_separable]	✓

5275	\[ {}y \left (1+2 y^{2}\right ) y^{\prime } = x \left (2 x^{2}+1\right ) \]	[_separable]	✓

5281	\[ {}x y^{3} y^{\prime } = \left (-x^{2}+1\right ) \left (1+y^{2}\right ) \]	[_separable]	✓

5311	\[ {}y^{\prime } \sqrt {b^{2}+y^{2}} = \sqrt {a^{2}+x^{2}} \]	[_separable]	✓

5312	\[ {}y^{\prime } \sqrt {-y^{2}+b^{2}} = \sqrt {a^{2}-x^{2}} \]	[_separable]	✓

5313	\[ {}y^{\prime } \sqrt {y} = \sqrt {x} \]	[_separable]	✓

5317	\[ {}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2} \]	[_separable]	✓

5318	\[ {}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2} \]	[_separable]	✓

5332	\[ {}y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right ) = 0 \]	[_separable]	✓

5345	\[ {}{y^{\prime }}^{2} = x^{2} y^{2} \]	[_separable]	✓

5404	\[ {}{y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+2 x y = 0 \]	[_quadrature]	✓

5406	\[ {}{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3} = 0 \]	[_separable]	✓

5409	\[ {}{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4} = 0 \]	[_separable]	✓

5411	\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0 \]	[_separable]	✓

5451	\[ {}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0 \]	[_quadrature]	✓

5455	\[ {}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0 \]	[_quadrature]	✓

5456	\[ {}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0 \]	[_quadrature]	✓

5476	\[ {}x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right ) = 0 \]	[_separable]	✓

5488	\[ {}x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y = 0 \]	[_separable]	✓

5501	\[ {}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y-y^{2} = 0 \]	[_separable]	✓

5527	\[ {}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0 \]	[_quadrature]	✓

5530	\[ {}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0 \]	[_quadrature]	✓

5552	\[ {}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0 \]	[_quadrature]	✓

5569	\[ {}4 y^{2} {y^{\prime }}^{2}+2 \left (3 x +1\right ) x y y^{\prime }+3 x^{3} = 0 \]	[_separable]	✓

5616	\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+x y+y^{2}\right ) y^{\prime }-x^{3} y^{3} = 0 \]	[_quadrature]	✓

5617	\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0 \]	[_quadrature]	✓

5624	\[ {}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0 \]	[_quadrature]	✓

5662	\[ {}2 \left (1+y\right )^{{3}/{2}}+3 y^{\prime } x -3 y = 0 \]	[_separable]	✓

5685	\[ {}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0 \]	[_separable]	✓

5699	\[ {}x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y = 0 \]	[_separable]	✓

5700	\[ {}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

5701	\[ {}x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2} = 0 \]	[_separable]	✓

5702	\[ {}1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 0 \]	[_separable]	✓

5703	\[ {}\sin \left (x \right ) \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

5704	\[ {}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

5717	\[ {}\left (-x^{2}+1\right ) z^{\prime }-x z = a x z^{2} \]	[_separable]	✓

5749	\[ {}\frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}} = -1 \]	[_separable]	✓

5770	\[ {}\frac {y-y^{\prime } x}{y^{\prime }+y^{2}} = \frac {y-y^{\prime } x}{1+x^{2} y^{\prime }} \]	[_separable]	✓

5791	\[ {}7 y-3+\left (2 x +1\right ) y^{\prime } = 0 \]	[_separable]	✓

5859	\[ {}y^{\prime }+\frac {y}{x} = \frac {y^{2}}{x} \] i.c.	[_separable]	✓

5870	\[ {}y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right ) \]	[_separable]	✓

5880	\[ {}2 y-y \ln \left (x \right ) x -2 x \ln \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

5886	\[ {}y^{\prime } x -y^{2}+1 = 0 \]	[_separable]	✓

5899	\[ {}\left (x^{2}-1\right ) y^{\prime }+x y-3 x y^{2} = 0 \]	[_separable]	✓

5900	\[ {}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0 \]	[_separable]	✓

5914	\[ {}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0 \]	[_separable]	✓

5915	\[ {}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0 \]	[_separable]	✓

6025	\[ {}y^{\prime }+y \tan \left (x \right ) = 0 \]	[_separable]	✓

6031	\[ {}x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y = 0 \]	[_separable]	✓

6032	\[ {}y^{\prime } = a x y^{2} \]	[_separable]	✓

6033	\[ {}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

6034	\[ {}x y \left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \]	[_separable]	✓

6035	\[ {}\frac {x}{1+y} = \frac {y y^{\prime }}{x +1} \]	[_separable]	✓

6037	\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \]	[_separable]	✓

6038	\[ {}\sin \left (x \right ) \cos \left (y\right ) = \cos \left (x \right ) \sin \left (y\right ) y^{\prime } \]	[_separable]	✓

6039	\[ {}a x y^{\prime }+2 y = x y^{\prime } y \]	[_separable]	✓

6093	\[ {}y^{\prime } x = y \] i.c.	[_separable]	✓

6094	\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \] i.c.	[_separable]	✓

6095	\[ {}y^{\prime } \sin \left (x \right ) = y \ln \left (y\right ) \] i.c.	[_separable]	✓

6096	\[ {}x y^{\prime } y+1+y^{2} = 0 \] i.c.	[_separable]	✓

6098	\[ {}y^{\prime } = \frac {2 x y^{2}+x}{x^{2} y-y} \] i.c.	[_separable]	✓

6099	\[ {}y y^{\prime }+x y^{2}-8 x = 0 \] i.c.	[_separable]	✓

6100	\[ {}y^{\prime }+2 x y^{2} = 0 \] i.c.	[_separable]	✓

6102	\[ {}y^{\prime }-x y = x \] i.c.	[_separable]	✓

6104	\[ {}\left (x +x y\right ) y^{\prime }+y = 0 \] i.c.	[_separable]	✓

6121	\[ {}3 x y^{2} y^{\prime }+3 y^{3} = 1 \]	[_separable]	✓

6209	\[ {}x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right ) = 0 \]	[_separable]	✓

6217	\[ {}u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime } = 0 \]	[_separable]	✓

6228	\[ {}y^{\prime }+x y = \frac {x}{y} \]	[_separable]	✓

6232	\[ {}3 x^{2} y+x^{3} y^{\prime } = 0 \] i.c.	[_separable]	✓

6237	\[ {}y^{\prime } x = x y+y \]	[_separable]	✓

6239	\[ {}y^{\prime } = 3 x^{2} y \]	[_separable]	✓

6241	\[ {}y^{\prime } x = y \]	[_separable]	✓

6259	\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{x +y}}{x^{2}+2} \]	[_separable]	✓

6260	\[ {}\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x = 0 \]	[_separable]	✓

6262	\[ {}y^{\prime } x = \frac {1}{y^{3}} \]	[_separable]	✓

6263	\[ {}x^{\prime } = 3 x t^{2} \]	[_separable]	✓

6264	\[ {}x^{\prime } = \frac {t \,{\mathrm e}^{-t -2 x}}{x} \]	[_separable]	✓

6265	\[ {}y^{\prime } = \frac {x}{y^{2} \sqrt {x +1}} \]	[_separable]	✓

6266	\[ {}x v^{\prime } = \frac {1-4 v^{2}}{3 v} \]	[_separable]	✓

6267	\[ {}y^{\prime } = \frac {\sec \left (y\right )^{2}}{x^{2}+1} \]	[_separable]	✓

6268	\[ {}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )^{{3}/{2}} \]	[_separable]	✓

6270	\[ {}x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime } = 0 \]	[_separable]	✓

6271	\[ {}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0 \]	[_separable]	✓

6272	\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right ) \] i.c.	[_separable]	✓

6273	\[ {}y^{\prime } = x^{3} \left (1-y\right ) \] i.c.	[_separable]	✓

6274	\[ {}\frac {y^{\prime }}{2} = \sqrt {1+y}\, \cos \left (x \right ) \] i.c.	[_separable]	✓

6275	\[ {}x^{2} y^{\prime } = \frac {4 x^{2}-x -2}{\left (x +1\right ) \left (1+y\right )} \] i.c.	[_separable]	✓

6276	\[ {}\frac {y^{\prime }}{\theta } = \frac {y \sin \left (\theta \right )}{y^{2}+1} \] i.c.	[_separable]	✓

6277	\[ {}x^{2}+2 y y^{\prime } = 0 \] i.c.	[_separable]	✓

6278	\[ {}y^{\prime } = 2 t \cos \left (y\right )^{2} \] i.c.	[_separable]	✓

6279	\[ {}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y} \] i.c.	[_separable]	✓

6280	\[ {}y^{\prime } = x^{2} \left (1+y\right ) \] i.c.	[_separable]	✓

6281	\[ {}\sqrt {y}+\left (x +1\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

6283	\[ {}y^{\prime } = \frac {{\mathrm e}^{x^{2}}}{y^{2}} \] i.c.	[_separable]	✓

6284	\[ {}y^{\prime } = \sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right ) \] i.c.	[_separable]	✓

6285	\[ {}y^{\prime } = 2 y-2 t y \] i.c.	[_separable]	✓

6288	\[ {}y^{\prime } = \left (x -3\right ) \left (1+y\right )^{{2}/{3}} \]	[_separable]	✓

6289	\[ {}y^{\prime } = x y^{3} \]	[_separable]	✓

6290	\[ {}y^{\prime } = x y^{3} \] i.c.	[_separable]	✓

6291	\[ {}y^{\prime } = x y^{3} \] i.c.	[_separable]	✓

6292	\[ {}y^{\prime } = x y^{3} \] i.c.	[_separable]	✓

6296	\[ {}\left (t^{2}+1\right ) y^{\prime } = t y-y \]	[_separable]	✓

6308	\[ {}\left (x^{2}+1\right ) y^{\prime }+x y-x = 0 \]	[_separable]	✓

6324	\[ {}\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime } = 0 \]	[_separable]	✓

6339	\[ {}y^{\prime } = \frac {{\mathrm e}^{x +y}}{-1+y} \]	[_separable]	✓

6343	\[ {}2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime } = 0 \]	[_separable]	✓

6344	\[ {}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]	[_separable]	✓

6405	\[ {}y^{\prime }+x y = x y^{2} \]	[_separable]	✓

6419	\[ {}\left (x +1\right )^{2} y^{\prime } = 1+y^{2} \]	[_separable]	✓

6423	\[ {}x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = 0 \]	[_separable]	✓

6425	\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y = x \]	[_separable]	✓

6430	\[ {}x \left (y-3\right ) y^{\prime } = 4 y \]	[_separable]	✓

6431	\[ {}\left (x^{3}+1\right ) y^{\prime } = x^{2} y \] i.c.	[_separable]	✓

6432	\[ {}x^{3}+\left (1+y\right )^{2} y^{\prime } = 0 \]	[_separable]	✓

6433	\[ {}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

6434	\[ {}x^{2} \left (1+y\right )+y^{2} \left (x -1\right ) y^{\prime } = 0 \]	[_separable]	✓

6456	\[ {}x y^{\prime } y-\left (x +1\right ) \sqrt {-1+y} = 0 \]	[_separable]	✓

6459	\[ {}y+\left (x^{2}-4 x \right ) y^{\prime } = 0 \]	[_separable]	✓

6462	\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (1+y\right ) \]	[_separable]	✓

6465	\[ {}y^{\prime } = {\mathrm e}^{3 x -2 y} \] i.c.	[_separable]	✓

6472	\[ {}y^{\prime }+x +x y^{2} = 0 \] i.c.	[_separable]	✓

6475	\[ {}x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime } = 0 \]	[_separable]	✓

6476	\[ {}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1 \] i.c.	[_separable]	✓

6569	\[ {}y^{\prime } x = 2 y \]	[_separable]	✓

6570	\[ {}y y^{\prime }+x = 0 \]	[_separable]	✓

6579	\[ {}4 y+y^{\prime } x = 0 \]	[_separable]	✓

6580	\[ {}1+2 y+\left (-x^{2}+4\right ) y^{\prime } = 0 \]	[_separable]	✓

6581	\[ {}y^{2}-x^{2} y^{\prime } = 0 \]	[_separable]	✓

6582	\[ {}1+y-\left (x +1\right ) y^{\prime } = 0 \]	[_separable]	✓

6588	\[ {}1+2 y-\left (4-x \right ) y^{\prime } = 0 \]	[_separable]	✓

6589	\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = 0 \]	[_separable]	✓

6593	\[ {}x y^{\prime } y = \left (1+y\right ) \left (1-x \right ) \]	[_separable]	✓

6596	\[ {}1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

6599	\[ {}y^{\prime } x +2 y = 0 \] i.c.	[_separable]	✓

6601	\[ {}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

6632	\[ {}1+y^{2} = \left (x^{2}+x \right ) y^{\prime } \]	[_separable]	✓

6642	\[ {}y^{\prime }-y = x y \]	[_separable]	✓

6651	\[ {}y y^{\prime }-x y^{2}+x = 0 \]	[_separable]	✓

6667	\[ {}x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (-1+y\right ) = 0 \]	[_quadrature]	✓

6885	\[ {}y^{2}-1+y^{\prime } x = 0 \]	[_separable]	✓

6892	\[ {}y^{\prime } = 2 x y^{2} \]	[_separable]	✓

6893	\[ {}2 y^{\prime } = y^{3} \cos \left (x \right ) \]	[_separable]	✓

6904	\[ {}y^{\prime } x -2 y = 0 \]	[_separable]	✓

6905	\[ {}y^{\prime } = -\frac {x}{y} \]	[_separable]	✓

6914	\[ {}3 y^{\prime } x +5 y = 10 \]	[_separable]	✓

6935	\[ {}y^{\prime }+2 x y^{2} = 0 \] i.c.	[_separable]	✓

6936	\[ {}y^{\prime }+2 x y^{2} = 0 \] i.c.	[_separable]	✓

6937	\[ {}y^{\prime }+2 x y^{2} = 0 \] i.c.	[_separable]	✓

6938	\[ {}y^{\prime }+2 x y^{2} = 0 \] i.c.	[_separable]	✓

6948	\[ {}y^{\prime } x = 2 y \] i.c.	[_separable]	✓

6951	\[ {}y^{\prime } x = y \]	[_separable]	✓

6953	\[ {}\left (4-y^{2}\right ) y^{\prime } = x^{2} \]	[_separable]	✓

6954	\[ {}\left (y^{3}+1\right ) y^{\prime } = x^{2} \]	[_separable]	✓

6961	\[ {}y^{\prime } x = y \] i.c.	[_separable]	✓

6968	\[ {}y y^{\prime } = 3 x \] i.c.	[_separable]	✓

6969	\[ {}y y^{\prime } = 3 x \] i.c.	[_separable]	✓

6970	\[ {}y y^{\prime } = 3 x \] i.c.	[_separable]	✓

6981	\[ {}y^{\prime } = x \sqrt {y} \] i.c.	[_separable]	✓

6985	\[ {}y^{\prime } x = y \]	[_separable]	✓

6990	\[ {}3 y^{\prime } x -2 y = 0 \]	[_separable]	✓

6991	\[ {}\left (-2+2 y\right ) y^{\prime } = 2 x -1 \] i.c.	[_separable]	✓

7004	\[ {}y^{\prime } x +y = \frac {1}{y^{2}} \]	[_separable]	✓

7026	\[ {}y^{\prime } = \sin \left (x \right ) \cos \left (y\right ) \] i.c.	[_separable]	✓

7027	\[ {}y^{\prime } = \sin \left (x \right ) \cos \left (y\right ) \] i.c.	[_separable]	✓

7028	\[ {}y^{\prime } = \sin \left (x \right ) \cos \left (y\right ) \] i.c.	[_separable]	✓

7029	\[ {}y^{\prime } = \sin \left (x \right ) \cos \left (y\right ) \] i.c.	[_separable]	✓

7034	\[ {}y y^{\prime } = -x \] i.c.	[_separable]	✓

7035	\[ {}y y^{\prime } = -x \] i.c.	[_separable]	✓

7040	\[ {}y^{\prime } = x \,{\mathrm e}^{y} \] i.c.	[_separable]	✓

7041	\[ {}y^{\prime } = x \,{\mathrm e}^{y} \] i.c.	[_separable]	✓

7067	\[ {}y^{\prime } x = 4 y \]	[_separable]	✓

7068	\[ {}y^{\prime }+2 x y^{2} = 0 \]	[_separable]	✓

7069	\[ {}y^{\prime } = {\mathrm e}^{3 x +2 y} \]	[_separable]	✓

7070	\[ {}y \,{\mathrm e}^{x} y^{\prime } = {\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \]	[_separable]	✓

7071	\[ {}y \ln \left (x \right ) y^{\prime } = \frac {\left (1+y\right )^{2}}{x^{2}} \]	[_separable]	✓

7072	\[ {}y^{\prime } = \frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \]	[_separable]	✓

7073	\[ {}\csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime } = 0 \]	[_separable]	✓

7074	\[ {}\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime } = 0 \]	[_separable]	✓

7075	\[ {}\left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime } = 0 \]	[_separable]	✓

7076	\[ {}x \sqrt {1+y^{2}} = y y^{\prime } \sqrt {x^{2}+1} \]	[_separable]	✓

7081	\[ {}y^{\prime } = \frac {x y+3 x -y-3}{x y-2 x +4 y-8} \]	[_separable]	✓

7082	\[ {}y^{\prime } = \frac {x y+2 y-x -2}{x y-3 y+x -3} \]	[_separable]	✓

7083	\[ {}y^{\prime } = x \sqrt {1-y^{2}} \]	[_separable]	✓

7084	\[ {}\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime } = y^{2} \]	[_separable]	✓

7086	\[ {}y^{\prime } = \frac {-1+y^{2}}{x^{2}-1} \] i.c.	[_separable]	✓

7087	\[ {}x^{2} y^{\prime } = y-x y \] i.c.	[_separable]	✓

7089	\[ {}\sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1} = 0 \] i.c.	[_separable]	✓

7090	\[ {}\left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right ) = 0 \] i.c.	[_separable]	✓

7092	\[ {}x \sinh \left (y\right ) y^{\prime } = \cosh \left (y\right ) \] i.c.	[_separable]	✓

7093	\[ {}y^{\prime } = {\mathrm e}^{-x^{2}} y \] i.c.	[_separable]	✓

7094	\[ {}y^{\prime } = y^{2} \sin \left (x^{2}\right ) \] i.c.	[_separable]	✓

7095	\[ {}y^{\prime } = \left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )} \] i.c.	[_separable]	✓

7096	\[ {}y^{\prime } = \frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1} \] i.c.	[_separable]	✓

7097	\[ {}y^{\prime } = \frac {3 x +1}{2 y} \] i.c.	[_separable]	✓

7098	\[ {}\left (-2+2 y\right ) y^{\prime } = 3 x^{2}+4 x +2 \] i.c.	[_separable]	✓

7099	\[ {}{\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime } = 0 \] i.c.	[_separable]	✓

7100	\[ {}\sin \left (x \right )+y y^{\prime } = 0 \] i.c.	[_separable]	✓

7104	\[ {}y^{\prime } x = y^{2}-y \] i.c.	[_separable]	✓

7105	\[ {}y^{\prime } x = y^{2}-y \] i.c.	[_separable]	✓

7106	\[ {}y^{\prime } x = y^{2}-y \] i.c.	[_separable]	✓

7107	\[ {}y^{\prime } x = y^{2}-y \] i.c.	[_separable]	✓

7108	\[ {}2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

7122	\[ {}y^{\prime } = \frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \]	[_separable]	✓

7123	\[ {}\left (\sqrt {x}+x \right ) y^{\prime } = \sqrt {y}+y \]	[_separable]	✓

7125	\[ {}y^{\prime } = \frac {{\mathrm e}^{\sqrt {x}}}{y} \] i.c.	[_separable]	✓

7126	\[ {}y^{\prime } = \frac {x \arctan \left (x \right )}{y} \] i.c.	[_separable]	✓

7127	\[ {}y^{\prime } = -\frac {x}{y} \] i.c.	[_separable]	✓

7128	\[ {}y^{\prime } = x \sqrt {y} \]	[_separable]	✓

7131	\[ {}y^{\prime } = y+\frac {y}{x \ln \left (x \right )} \] i.c.	[_separable]	✓

7138	\[ {}y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \] i.c.	[_separable]	✓

7139	\[ {}y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \] i.c.	[_separable]	✓

7140	\[ {}y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \] i.c.	[_separable]	✓

7141	\[ {}y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \] i.c.	[_separable]	✓

7142	\[ {}\left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x = 0 \] i.c.	[_separable]	✓

7143	\[ {}y^{\prime } = \frac {x \left (1-x \right )}{y \left (-2+y\right )} \] i.c.	[_separable]	✓

7144	\[ {}y^{\prime } = \frac {x \left (1-x \right )}{y \left (-2+y\right )} \] i.c.	[_separable]	✓

7149	\[ {}y^{\prime }+3 x^{2} y = x^{2} \]	[_separable]	✓

7154	\[ {}y^{\prime } x +2 y = 3 \]	[_separable]	✓

7166	\[ {}p^{\prime }+2 t p = p+4 t -2 \]	[_separable]	✓

7179	\[ {}y^{\prime }-y \sin \left (x \right ) = 2 \sin \left (x \right ) \] i.c.	[_separable]	✓

7186	\[ {}y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y = 0 \] i.c.	[_separable]	✓

7192	\[ {}y^{\prime }-\sin \left (x^{2}\right ) y = 0 \] i.c.	[_separable]	✓

7200	\[ {}2 x -1+\left (3 y+7\right ) y^{\prime } = 0 \]	[_separable]	✓

7382	\[ {}y^{\prime } = \frac {x^{2}}{y} \]	[_separable]	✓

7383	\[ {}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y} \]	[_separable]	✓

7384	\[ {}y^{\prime } = y \sin \left (x \right ) \]	[_separable]	✓

7385	\[ {}y^{\prime } x = \sqrt {1-y^{2}} \]	[_separable]	✓

7386	\[ {}y^{\prime } = \frac {x^{2}}{1+y^{2}} \]	[_separable]	✓

7387	\[ {}x y^{\prime } y = \sqrt {1+y^{2}} \]	[_separable]	✓

7388	\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0 \] i.c.	[_separable]	✓

7390	\[ {}y^{\prime } x +y = y^{2} \] i.c.	[_separable]	✓

7391	\[ {}2 x^{2} y y^{\prime }+y^{2} = 2 \]	[_separable]	✓

7392	\[ {}y^{\prime }-x y^{2} = 2 x y \]	[_separable]	✓

7394	\[ {}y^{\prime } = \frac {3 x^{2}+4 x +2}{-2+2 y} \] i.c.	[_separable]	✓

7395	\[ {}{\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime } = 0 \] i.c.	[_separable]	✓

7396	\[ {}\frac {y}{x -1}+\frac {x y^{\prime }}{1+y} = 0 \]	[_separable]	✓

7397	\[ {}x +2 x^{3}+\left (2 y^{3}+y\right ) y^{\prime } = 0 \]	[_separable]	✓

7398	\[ {}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0 \]	[_separable]	✓

7399	\[ {}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0 \]	[_separable]	✓

7400	\[ {}2 x \sqrt {1-y^{2}}+y y^{\prime } = 0 \]	[_separable]	✓

7401	\[ {}y^{\prime } = \left (-1+y\right ) \left (x +1\right ) \]	[_separable]	✓

7402	\[ {}y^{\prime } = {\mathrm e}^{x -y} \]	[_separable]	✓

7403	\[ {}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}} \]	[_separable]	✓

7404	\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \]	[_separable]	✓

7405	\[ {}z^{\prime } = 10^{x +z} \]	[_separable]	✓

7415	\[ {}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

7416	\[ {}\left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (1+y\right ) y^{\prime } = 0 \]	[_separable]	✓

7418	\[ {}y-2 x y+x^{2} y^{\prime } = 0 \]	[_separable]	✓

7476	\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \]	[_separable]	✓

7502	\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \]	[_separable]	✓

7503	\[ {}y^{\prime } = \frac {x^{2}}{1-y^{2}} \]	[_separable]	✓

7504	\[ {}y^{\prime } = \frac {3 x^{2}+4 x +2}{-2+2 y} \] i.c.	[_separable]	✓

7512	\[ {}y^{\prime } = -\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \]	[_separable]	✓

7555	\[ {}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0 \]	[_separable]	✓

7583	\[ {}y^{\prime }+\cos \left (x \right ) y = 0 \]	[_separable]	✓

7601	\[ {}y^{\prime }+2 x y = x \]	[_separable]	✓

7603	\[ {}y^{\prime }+y \,{\mathrm e}^{x} = 3 \,{\mathrm e}^{x} \]	[_separable]	✓

7731	\[ {}y^{\prime } = x^{2} y \]	[_separable]	✓

7732	\[ {}y y^{\prime } = x \]	[_separable]	✓

7733	\[ {}y^{\prime } = \frac {x^{2}+x}{y-y^{2}} \]	[_separable]	✓

7734	\[ {}y^{\prime } = \frac {{\mathrm e}^{x -y}}{{\mathrm e}^{x}+1} \]	[_separable]	✓

7735	\[ {}y^{\prime } = x^{2} y^{2}-4 x^{2} \]	[_separable]	✓

7774	\[ {}y^{\prime } x = 2 y \]	[_separable]	✓

7775	\[ {}y y^{\prime } = {\mathrm e}^{2 x} \]	[_separable]	✓

7807	\[ {}x^{5} y^{\prime }+y^{5} = 0 \]	[_separable]	✓

7808	\[ {}y^{\prime } = 4 x y \]	[_separable]	✓

7809	\[ {}y^{\prime }+y \tan \left (x \right ) = 0 \]	[_separable]	✓

7810	\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]	[_separable]	✓

7811	\[ {}y \ln \left (y\right )-y^{\prime } x = 0 \]	[_separable]	✓

7812	\[ {}y^{\prime } x = \left (-4 x^{2}+1\right ) \tan \left (y\right ) \]	[_separable]	✓

7813	\[ {}y^{\prime } \sin \left (y\right ) = x^{2} \]	[_separable]	✓

7814	\[ {}y^{\prime }-y \tan \left (x \right ) = 0 \]	[_separable]	✓

7815	\[ {}x y^{\prime } y = -1+y \]	[_separable]	✓

7816	\[ {}x y^{2}-x^{2} y^{\prime } = 0 \]	[_separable]	✓

7817	\[ {}y y^{\prime } = x +1 \] i.c.	[_separable]	✓

7818	\[ {}x^{2} y^{\prime } = y \] i.c.	[_separable]	✓

7819	\[ {}\frac {y^{\prime }}{x^{2}+1} = \frac {x}{y} \] i.c.	[_separable]	✓

7820	\[ {}y^{2} y^{\prime } = x +2 \] i.c.	[_separable]	✓

7821	\[ {}y^{\prime } = x^{2} y^{2} \] i.c.	[_separable]	✓

7822	\[ {}\left (1+y\right ) y^{\prime } = -x^{2}+1 \] i.c.	[_separable]	✓

7844	\[ {}y^{\prime }+x y = x y^{4} \]	[_separable]	✓

7848	\[ {}y^{\prime } x = 2 x^{2} y+y \ln \left (x \right ) \]	[_separable]	✓

7854	\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]	[_separable]	✓

7855	\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

7858	\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \]	[_separable]	✓

7864	\[ {}\ln \left (y\right ) x +x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \]	[_separable]	✓

7919	\[ {}x^{2} y^{\prime } = y \]	[_separable]	✓

7920	\[ {}\sec \left (x \right ) y^{\prime } = \sec \left (y\right ) \]	[_separable]	✓

7923	\[ {}x^{2} y^{\prime }+2 x y = 0 \]	[_separable]	✓

7924	\[ {}-\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

7927	\[ {}y^{2} y^{\prime } = x \] i.c.	[_separable]	✓

7928	\[ {}\csc \left (x \right ) y^{\prime } = \csc \left (y\right ) \] i.c.	[_separable]	✓

7931	\[ {}2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

7932	\[ {}\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} = 0 \]	[_separable]	✓

8073	\[ {}y^{\prime } = 2 x y \]	[_separable]	✓

8085	\[ {}y^{\prime } x = y \]	[_separable]	✓

8087	\[ {}x^{2} y^{\prime } = y \]	[_separable]	✓

8436	\[ {}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0 \]	[_quadrature]	✓

8438	\[ {}x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y = 0 \]	[_separable]	✓

8439	\[ {}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0 \]	[_quadrature]	✓

8440	\[ {}{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0 \]	[_quadrature]	✓

8442	\[ {}{y^{\prime }}^{2}-x^{2} y^{2} = 0 \]	[_separable]	✓

8444	\[ {}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0 \]	[_quadrature]	✓

8445	\[ {}{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3} = 0 \]	[_separable]	✓

8448	\[ {}x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y = 0 \]	[_quadrature]	✓

8452	\[ {}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0 \]	[_quadrature]	✓

8534	\[ {}6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y = 0 \]	[_quadrature]	✓

8539	\[ {}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0 \]	[_quadrature]	✓

8553	\[ {}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0 \]	[_quadrature]	✓

8697	\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \]	[_separable]	✓

8698	\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \] i.c.	[_separable]	✓

8713	\[ {}y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x} \]	[_separable]	✓

8714	\[ {}y^{\prime } = x \left (\cos \left (y\right )+y\right ) \]	[_separable]	✓

8715	\[ {}y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \]	[_separable]	✓

8716	\[ {}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \]	[_separable]	✓

8724	\[ {}y^{\prime } = \frac {2 y}{x} \] i.c.	[_separable]	✓

8725	\[ {}y^{\prime } = \frac {2 y}{x} \]	[_separable]	✓

8726	\[ {}y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )} \]	[_separable]	✓

8735	\[ {}y = y^{\prime } x +x^{2} {y^{\prime }}^{2} \]	[_separable]	✓

8792	\[ {}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \]	[_separable]	✓

8982	\[ {}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0 \]	[_separable]	✓

8990	\[ {}y^{\prime } = y a x \]	[_separable]	✓

9036	\[ {}{y^{\prime }}^{2} = \frac {y^{2}}{x} \]	[_separable]	✓

9050	\[ {}y^{\prime } = {\mathrm e}^{x +y} \]	[_separable]	✓

10023	\[ {}y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y = 0 \]	[_separable]	✓

10043	\[ {}y^{\prime }-x y^{2}-3 x y = 0 \]	[_separable]	✓

10045	\[ {}y^{\prime }-a \,x^{n} \left (1+y^{2}\right ) = 0 \]	[_separable]	✓

10049	\[ {}y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right ) = 0 \]	[_separable]	✓

10073	\[ {}y^{\prime }-\frac {\sqrt {-1+y^{2}}}{\sqrt {x^{2}-1}} = 0 \]	[_separable]	✓

10074	\[ {}y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {-1+y^{2}}} = 0 \]	[_separable]	✓

10076	\[ {}y^{\prime }-\frac {1+y^{2}}{{\| y+\sqrt {1+y}\|} \left (x +1\right )^{{3}/{2}}} = 0 \]	[_separable]	✓

10079	\[ {}y^{\prime }-\frac {\sqrt {{\| y \left (-1+y\right ) \left (-1+a y\right )\|}}}{\sqrt {{\| x \left (x -1\right ) \left (a x -1\right )\|}}} = 0 \]	[_separable]	✓

10080	\[ {}y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}} = 0 \]	[_separable]	✓

10085	\[ {}y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+x^{3} a_{3} +x^{2} a_{2} +a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right ) = 0 \]	[_separable]	✓

10088	\[ {}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0 \]	[_separable]	✓

10108	\[ {}y^{\prime } x -y^{2}+1 = 0 \]	[_separable]	✓

10129	\[ {}y^{\prime } x -y \ln \left (y\right ) = 0 \]	[_separable]	✓

10142	\[ {}\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0 \]	[_separable]	✓

10146	\[ {}x^{2} y^{\prime }-\left (x -1\right ) y = 0 \]	[_separable]	✓

10169	\[ {}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0 \]	[_separable]	✓

10170	\[ {}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0 \]	[_separable]	✓

10185	\[ {}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0 \]	[_separable]	✓

10194	\[ {}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0 \]	[_separable]	✓

10201	\[ {}\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {-1+y^{2}} = 0 \]	[_separable]	✓

10202	\[ {}y^{\prime } \sqrt {-x^{2}+1}-y \sqrt {-1+y^{2}} = 0 \]	[_separable]	✓

10210	\[ {}y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right ) = 0 \]	[_separable]	✓

10220	\[ {}y y^{\prime }+x y^{2}-4 x = 0 \]	[_separable]	✓

10251	\[ {}2 x y^{\prime } y+2 y^{2}+1 = 0 \]	[_separable]	✓

10265	\[ {}x^{2} \left (-1+y\right ) y^{\prime }+\left (x -1\right ) y = 0 \]	[_separable]	✓

10316	\[ {}2 y^{3} y^{\prime }+x y^{2} = 0 \]	[_separable]	✓

10317	\[ {}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0 \]	[_separable]	✓

10342	\[ {}\sqrt {-1+y^{2}}\, y^{\prime }-\sqrt {x^{2}-1} = 0 \]	[_separable]	✓

10354	\[ {}y^{\prime } \left (1+\sin \left (x \right )\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right ) = 0 \]	[_separable]	✓

10360	\[ {}x \cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 0 \]	[_separable]	✓

10365	\[ {}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

10366	\[ {}3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y = 0 \]	[_separable]	✓

10398	\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0 \]	[_separable]	✓

10399	\[ {}{y^{\prime }}^{2}+y \left (y-x \right ) y^{\prime }-x y^{3} = 0 \]	[_separable]	✓

10442	\[ {}x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+3 y^{2} = 0 \]	[_separable]	✓

10444	\[ {}x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y = 0 \]	[_separable]	✓

10445	\[ {}x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 x y+x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right ) = 0 \]	[_linear]	✓

10451	\[ {}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+y^{2} = 0 \]	[_separable]	✓

10472	\[ {}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0 \]	[_quadrature]	✓

10526	\[ {}{y^{\prime }}^{2}-a x y y^{\prime }+2 a y^{2} = 0 \]	[_separable]	✓

10527	\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0 \]	[_quadrature]	✓

10552	\[ {}{y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1} = 0 \]	[_separable]	✓

10566	\[ {}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0 \]	[_separable]	✓

11924	\[ {}y^{\prime } = f \left (x \right ) g \left (y\right ) \]	[_separable]	✓

12732	\[ {}\sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

12733	\[ {}\left (x +1\right ) y^{2}-x^{3} y^{\prime } = 0 \]	[_separable]	✓

12734	\[ {}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right ) = 0 \]	[_separable]	✓

12735	\[ {}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0 \]	[_separable]	✓

12740	\[ {}y^{3}+x^{3} y^{\prime } = 0 \]	[_separable]	✓

12754	\[ {}y y^{\prime }+x y^{2} = x \]	[_separable]	✓

12755	\[ {}y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right ) \]	[_separable]	✓

12759	\[ {}y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right ) = 0 \]	[_separable]	✓

12770	\[ {}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0 \]	[_separable]	✓

12776	\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \]	[_separable]	✓

12777	\[ {}y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0 \]	[_separable]	✓

12781	\[ {}x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0 \]	[_separable]	✓

12788	\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \]	[_separable]	✓

12794	\[ {}\left (1-x \right ) y-x \left (1+y\right ) y^{\prime } = 0 \]	[_separable]	✓

12795	\[ {}3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime } = 0 \]	[_separable]	✓

12836	\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2} \]	[_separable]	✓

12838	\[ {}x^{2} {y^{\prime }}^{2}-2 \left (x y+2 y^{\prime }\right ) y^{\prime }+y^{2} = 0 \]	[_separable]	✓

12954	\[ {}x^{\prime } = \frac {2 x}{t} \]	[_separable]	✓

12955	\[ {}x^{\prime } = -\frac {t}{x} \]	[_separable]	✓

12960	\[ {}2 t x^{\prime } = x \]	[_separable]	✓

12981	\[ {}x^{\prime } = \frac {2 x}{1+t} \]	[_separable]	✓

12982	\[ {}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \]	[_separable]	✓

12983	\[ {}\left (2 u+1\right ) u^{\prime }-1-t = 0 \]	[_separable]	✓

12984	\[ {}R^{\prime } = \left (1+t \right ) \left (1+R^{2}\right ) \]	[_separable]	✓

12986	\[ {}\left (1+t \right ) x^{\prime }+x^{2} = 0 \]	[_separable]	✓

12989	\[ {}x^{\prime } = 2 t x^{2} \] i.c.	[_separable]	✓

12990	\[ {}x^{\prime } = t^{2} {\mathrm e}^{-x} \] i.c.	[_separable]	✓

12992	\[ {}x^{\prime } = {\mathrm e}^{t +x} \] i.c.	[_separable]	✓

12993	\[ {}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \] i.c.	[_separable]	✓

12994	\[ {}y^{\prime } = t^{2} \tan \left (y\right ) \] i.c.	[_separable]	✓

12995	\[ {}x^{\prime } = \frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \] i.c.	[_separable]	✓

12996	\[ {}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1} \] i.c.	[_separable]	✓

12997	\[ {}x^{\prime } = \frac {t^{2}}{1-x^{2}} \] i.c.	[_separable]	✓

12998	\[ {}x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}} \]	[_separable]	✓

13003	\[ {}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}} \] i.c.	[_separable]	✓

13005	\[ {}\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right ) = 0 \]	[_separable]	✓

13015	\[ {}\left (t^{2}+1\right ) x^{\prime } = -3 t x+6 t \]	[_separable]	✓

13017	\[ {}x^{\prime } = \left (a +\frac {b}{t}\right ) x \] i.c.	[_separable]	✓

13020	\[ {}\cos \left (\theta \right ) v^{\prime }+v = 3 \]	[_separable]	✓

13023	\[ {}x^{\prime } = 2 t x \]	[_separable]	✓

13028	\[ {}x^{\prime }+p \left (t \right ) x = 0 \]	[_separable]	✓

13031	\[ {}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}} \]	[_separable]	✓

13035	\[ {}x^{3}+3 t x^{2} x^{\prime } = 0 \]	[_separable]	✓

13038	\[ {}x+3 t x^{2} x^{\prime } = 0 \]	[_separable]	✓

13039	\[ {}x^{2}-t^{2} x^{\prime } = 0 \]	[_separable]	✓

13040	\[ {}t \cot \left (x\right ) x^{\prime } = -2 \]	[_separable]	✓

13182	\[ {}y^{\prime }+4 x y = 8 x \]	[_separable]	✓

13198	\[ {}y^{\prime } = x^{2} \sin \left (y\right ) \] i.c.	[_separable]	✓

13199	\[ {}y^{\prime } = \frac {y^{2}}{x -2} \] i.c.	[_separable]	✓

13208	\[ {}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0 \]	[_separable]	✓

13219	\[ {}\left (x^{2}+1\right ) y^{\prime }+4 x y = 0 \]	[_separable]	✓

13220	\[ {}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0 \]	[_separable]	✓

13221	\[ {}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0 \]	[_separable]	✓

13222	\[ {}\csc \left (y\right )+\sec \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

13223	\[ {}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0 \]	[_separable]	✓

13224	\[ {}\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0 \]	[_separable]	✓

13225	\[ {}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0 \]	[_separable]	✓

13233	\[ {}y+2+y \left (x +4\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

13234	\[ {}8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0 \] i.c.	[_separable]	✓

13235	\[ {}\left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

13246	\[ {}y^{\prime }+4 x y = 8 x \]	[_separable]	✓

13247	\[ {}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}} \]	[_separable]	✓

13248	\[ {}\left (u^{2}+1\right ) v^{\prime }+4 u v = 3 u \]	[_separable]	✓

13257	\[ {}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x} \]	[_separable]	✓

13259	\[ {}y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0 \]	[_separable]	✓

13260	\[ {}x^{\prime }+\frac {\left (1+t \right ) x}{2 t} = \frac {1+t}{t x} \]	[_separable]	✓

13262	\[ {}y^{\prime }+3 x^{2} y = x^{2} \] i.c.	[_separable]	✓

13264	\[ {}2 x \left (1+y\right )-\left (x^{2}+1\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

13276	\[ {}\left (1+y\right ) y^{\prime }+x \left (2 y+y^{2}\right ) = x \]	[_separable]	✓

13280	\[ {}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0 \]	[_separable]	✓

13282	\[ {}y-1+x \left (x +1\right ) y^{\prime } = 0 \]	[_separable]	✓

13285	\[ {}y^{2} {\mathrm e}^{2 x}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime } = 0 \]	[_separable]	✓

13286	\[ {}8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0 \]	[_separable]	✓

13291	\[ {}x y+x^{2} y^{\prime } = x y^{3} \]	[_separable]	✓

13292	\[ {}\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y = 6 x^{2} \]	[_separable]	✓

13295	\[ {}8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime } = 0 \] i.c.	[_separable]	✓

13298	\[ {}4 x y^{\prime } y = 1+y^{2} \] i.c.	[_separable]	✓

13300	\[ {}y^{\prime } = \frac {x y}{x^{2}+1} \] i.c.	[_separable]	✓

13648	\[ {}x^{\prime } = t^{3} \left (1-x\right ) \] i.c.	[_separable]	✓

13649	\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right ) \] i.c.	[_separable]	✓

13650	\[ {}x^{\prime } = x t^{2} \]	[_separable]	✓

13652	\[ {}y^{\prime } = y^{2} {\mathrm e}^{-t^{2}} \]	[_separable]	✓

13654	\[ {}y^{\prime } x = k y \]	[_separable]	✓

13655	\[ {}i^{\prime } = p \left (t \right ) i \]	[_separable]	✓

13661	\[ {}x^{\prime }+t x = 4 t \] i.c.	[_separable]	✓

13674	\[ {}V^{\prime }\left (x \right )+2 y y^{\prime } = 0 \]	[_separable]	✓

13675	\[ {}\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b = 0 \]	[_separable]	✓

13777	\[ {}\tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

13784	\[ {}y^{\prime } = {\mathrm e}^{x -y} \]	[_separable]	✓

13791	\[ {}y = y^{\prime } x +\frac {1}{y} \]	[_separable]	✓

13828	\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0 \]	[_separable]	✓

13877	\[ {}y^{\prime } = y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \]	[_separable]	✓

13878	\[ {}x^{2} y^{\prime } = 1+y^{2} \]	[_separable]	✓

13880	\[ {}x \left ({\mathrm e}^{y}+4\right ) = {\mathrm e}^{x +y} y^{\prime } \]	[_separable]	✓

13884	\[ {}y^{\prime } = x \,{\mathrm e}^{-x +y^{2}} \]	[_separable]	✓

13886	\[ {}x \left (1+y\right )^{2} = \left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \]	[_separable]	✓

13897	\[ {}5 y^{\prime }-x y = 0 \]	[_separable]	✓

14091	\[ {}y-y^{\prime } x = 0 \]	[_separable]	✓

14092	\[ {}\left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0 \]	[_separable]	✓

14093	\[ {}1+y-\left (1-x \right ) y^{\prime } = 0 \]	[_separable]	✓

14094	\[ {}\left (t^{2}+x t^{2}\right ) x^{\prime }+x^{2}+t x^{2} = 0 \]	[_separable]	✓

14095	\[ {}y-a +x^{2} y^{\prime } = 0 \]	[_separable]	✓

14096	\[ {}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0 \]	[_separable]	✓

14097	\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \]	[_separable]	✓

14098	\[ {}1+s^{2}-\sqrt {t}\, s^{\prime } = 0 \]	[_separable]	✓

14099	\[ {}r^{\prime }+r \tan \left (t \right ) = 0 \]	[_separable]	✓

14100	\[ {}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0 \]	[_separable]	✓

14101	\[ {}y^{\prime } \sqrt {-x^{2}+1}-\sqrt {1-y^{2}} = 0 \]	[_separable]	✓

14102	\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]	[_separable]	✓

14103	\[ {}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

14130	\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0 \]	[_separable]	✓

14142	\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \]	[_separable]	✓

14150	\[ {}y = y^{\prime } x +y^{\prime } \]	[_separable]	✓

14205	\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \]	[_separable]	✓

14213	\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]	[_separable]	✓

14240	\[ {}y^{\prime } x -y = 0 \]	[_separable]	✓

14247	\[ {}x^{2} y^{\prime }+2 x y = 0 \]	[_separable]	✓

14255	\[ {}2 y^{\prime } x -y = 0 \]	[_separable]	✓

14262	\[ {}y^{\prime }-2 x y = 0 \]	[_separable]	✓

14265	\[ {}y^{\prime } = x \sqrt {y} \]	[_separable]	✓

14268	\[ {}x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y = 0 \]	[_separable]	✓

14286	\[ {}y^{\prime } = x y \]	[_separable]	✓

14287	\[ {}y^{\prime } = -x y \]	[_separable]	✓

14291	\[ {}y^{\prime } = x y \]	[_separable]	✓

14292	\[ {}y^{\prime } = \frac {x}{y} \]	[_separable]	✓

14293	\[ {}y^{\prime } = \frac {y}{x} \]	[_separable]	✓

14298	\[ {}y^{\prime } = {\mathrm e}^{x -y} \]	[_separable]	✓

14304	\[ {}y^{\prime } = \frac {1}{x y} \]	[_separable]	✓

14308	\[ {}y^{\prime } = \frac {x}{y^{2}} \]	[_separable]	✓

14309	\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \]	[_separable]	✓

14310	\[ {}y^{\prime } = \frac {x y}{1-y} \]	[_separable]	✓

14324	\[ {}y^{\prime } = -x \sqrt {1-y^{2}} \] i.c.	[_separable]	✓

14339	\[ {}y^{\prime } = x \,{\mathrm e}^{y-x^{2}} \] i.c.	[_separable]	✓

14340	\[ {}y^{\prime } = \frac {y}{x} \] i.c.	[_separable]	✓

14341	\[ {}y^{\prime } = \frac {2 x}{y} \] i.c.	[_separable]	✓

14343	\[ {}y^{\prime } = x +x y \] i.c.	[_separable]	✓

14344	\[ {}x \,{\mathrm e}^{y}+y^{\prime } = 0 \] i.c.	[_separable]	✓

14345	\[ {}y-x^{2} y^{\prime } = 0 \] i.c.	[_separable]	✓

14347	\[ {}2 x y^{\prime } y+y^{2} = -1 \]	[_separable]	✓

14353	\[ {}y^{\prime } = \frac {y}{x} \] i.c.	[_separable]	✓

14358	\[ {}x -y y^{\prime } = 0 \]	[_separable]	✓

14359	\[ {}y-y^{\prime } x = 0 \]	[_separable]	✓

14361	\[ {}x y \left (1-y\right )-2 y^{\prime } = 0 \]	[_separable]	✓

14362	\[ {}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0 \]	[_separable]	✓

14363	\[ {}\left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime } = 0 \]	[_separable]	✓

14366	\[ {}y^{\prime } = \frac {y}{x} \] i.c.	[_separable]	✓

14367	\[ {}y^{\prime } = \frac {y}{x} \] i.c.	[_separable]	✓

14377	\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] i.c.	[_separable]	✓

14378	\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] i.c.	[_separable]	✓

14379	\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] i.c.	[_separable]	✓

14380	\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] i.c.	[_separable]	✓

14381	\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] i.c.	[_separable]	✓

14382	\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] i.c.	[_separable]	✓

14383	\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] i.c.	[_separable]	✓

14384	\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] i.c.	[_separable]	✓

14385	\[ {}y^{\prime } = 3 x y^{{1}/{3}} \] i.c.	[_separable]	✓

14386	\[ {}y^{\prime } = 3 x y^{{1}/{3}} \] i.c.	[_separable]	✓

14387	\[ {}y^{\prime } = 3 x y^{{1}/{3}} \] i.c.	[_separable]	✓

14388	\[ {}y^{\prime } = 3 x y^{{1}/{3}} \] i.c.	[_separable]	✓

14389	\[ {}y^{\prime } = 3 x y^{{1}/{3}} \] i.c.	[_separable]	✓

14400	\[ {}y^{\prime } = x \sqrt {1-y^{2}} \] i.c.	[_separable]	✓

14401	\[ {}y^{\prime } = x \sqrt {1-y^{2}} \] i.c.	[_separable]	✓

14402	\[ {}y^{\prime } = x \sqrt {1-y^{2}} \] i.c.	[_separable]	✓

14403	\[ {}y^{\prime } = x \sqrt {1-y^{2}} \] i.c.	[_separable]	✓

14530	\[ {}y^{\prime } = \frac {1+y}{1+t} \]	[_separable]	✓

14531	\[ {}y^{\prime } = t^{2} y^{2} \]	[_separable]	✓

14532	\[ {}y^{\prime } = t^{4} y \]	[_separable]	✓

14537	\[ {}y^{\prime } = 2 t y^{2}+3 y^{2} \]	[_separable]	✓

14538	\[ {}y^{\prime } = \frac {t}{y} \]	[_separable]	✓

14539	\[ {}y^{\prime } = \frac {t}{y+t^{2} y} \]	[_separable]	✓

14540	\[ {}y^{\prime } = t y^{{1}/{3}} \]	[_separable]	✓

14542	\[ {}y^{\prime } = \frac {2 y+1}{t} \]	[_separable]	✓

14544	\[ {}y^{\prime } = \frac {4 t}{1+3 y^{2}} \]	[_separable]	✓

14545	\[ {}v^{\prime } = t^{2} v-2-2 v+t^{2} \]	[_separable]	✓

14546	\[ {}y^{\prime } = \frac {1}{t y+t +y+1} \]	[_separable]	✓

14547	\[ {}y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}} \]	[_separable]	✓

14549	\[ {}w^{\prime } = \frac {w}{t} \]	[_separable]	✓

14551	\[ {}x^{\prime } = -t x \] i.c.	[_separable]	✓

14552	\[ {}y^{\prime } = t y \] i.c.	[_separable]	✓

14554	\[ {}y^{\prime } = t^{2} y^{3} \] i.c.	[_separable]	✓

14556	\[ {}y^{\prime } = \frac {t}{y-t^{2} y} \] i.c.	[_separable]	✓

14558	\[ {}y^{\prime } = t y^{2}+2 y^{2} \] i.c.	[_separable]	✓

14559	\[ {}x^{\prime } = \frac {t^{2}}{x+t^{3} x} \] i.c.	[_separable]	✓

14561	\[ {}y^{\prime } = \left (1+y^{2}\right ) t \] i.c.	[_separable]	✓

14563	\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] i.c.	[_separable]	✓

14574	\[ {}y^{\prime } = \left (1+t \right ) y \] i.c.	[_separable]	✓

14584	\[ {}y^{\prime } = t y+t y^{2} \]	[_separable]	✓

14585	\[ {}y^{\prime } = t^{2}+t^{2} y \]	[_separable]	✓

14586	\[ {}y^{\prime } = t +t y \]	[_separable]	✓

14613	\[ {}y^{\prime } = \frac {1}{\left (1+y\right ) \left (t -2\right )} \] i.c.	[_separable]	✓

14615	\[ {}y^{\prime } = \frac {t}{-2+y} \] i.c.	[_separable]	✓

14697	\[ {}y^{\prime } = \frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \]	[_separable]	✓

14702	\[ {}y^{\prime } = t y \]	[_separable]	✓

14704	\[ {}y^{\prime } = \frac {t y}{t^{2}+1} \]	[_separable]	✓

14710	\[ {}x^{\prime } = -t x \] i.c.	[_separable]	✓

14713	\[ {}y^{\prime } = t^{2} y^{3}+y^{3} \] i.c.	[_separable]	✓

14716	\[ {}y^{\prime } = \frac {\left (1+t \right )^{2}}{\left (1+y\right )^{2}} \] i.c.	[_separable]	✓

14717	\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] i.c.	[_separable]	✓

14719	\[ {}y^{\prime } = \frac {t^{2}}{y+t^{3} y} \] i.c.	[_separable]	✓

14723	\[ {}y^{\prime } = t^{2} y+1+y+t^{2} \]	[_separable]	✓

14724	\[ {}y^{\prime } = \frac {2 y+1}{t} \]	[_separable]	✓

14912	\[ {}y y^{\prime } = 2 x \]	[_separable]	✓

14953	\[ {}y^{\prime }+3 x y = 6 x \]	[_separable]	✓

14956	\[ {}x^{2} y^{\prime }+x y^{2} = x \]	[_separable]	✓

14959	\[ {}\left (x -2\right ) y^{\prime } = 3+y \]	[_separable]	✓

14960	\[ {}\left (-2+y\right ) y^{\prime } = x -3 \]	[_separable]	✓

14964	\[ {}y^{\prime } = 3 y^{2}-\sin \left (x \right ) y^{2} \]	[_separable]	✓

14969	\[ {}y^{\prime }+x y = 4 x \]	[_separable]	✓

14971	\[ {}y^{\prime } = x y-3 x -2 y+6 \]	[_separable]	✓

14973	\[ {}y y^{\prime } = {\mathrm e}^{x -3 y^{2}} \]	[_separable]	✓

14974	\[ {}y^{\prime } = \frac {x}{y} \]	[_separable]	✓

14976	\[ {}x y^{\prime } y = y^{2}+9 \]	[_separable]	✓

14977	\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \]	[_separable]	✓

14978	\[ {}y^{\prime } \cos \left (y\right ) = \sin \left (x \right ) \]	[_separable]	✓

14979	\[ {}y^{\prime } = {\mathrm e}^{2 x -3 y} \]	[_separable]	✓

14980	\[ {}y^{\prime } = \frac {x}{y} \] i.c.	[_separable]	✓

14981	\[ {}y^{\prime } = 2 x -1+2 x y-y \] i.c.	[_separable]	✓

14982	\[ {}y y^{\prime } = x y^{2}+x \] i.c.	[_separable]	✓

14984	\[ {}y^{\prime } = x y-4 x \]	[_separable]	✓

14986	\[ {}y y^{\prime } = x y^{2}-9 x \]	[_separable]	✓

14988	\[ {}y^{\prime } = {\mathrm e}^{x +y^{2}} \]	[_separable]	✓

14990	\[ {}y^{\prime } = x y-4 x \]	[_separable]	✓

14991	\[ {}y^{\prime } = x y-3 x -2 y+6 \]	[_separable]	✓

14992	\[ {}y^{\prime } = 3 y^{2}-\sin \left (x \right ) y^{2} \]	[_separable]	✓

14994	\[ {}y^{\prime } = \frac {y}{x} \]	[_separable]	✓

14995	\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \]	[_separable]	✓

14996	\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \]	[_separable]	✓

14997	\[ {}\left (-1+y^{2}\right ) y^{\prime } = 4 x y^{2} \]	[_separable]	✓

15000	\[ {}y^{\prime } = 3 x y^{3} \]	[_separable]	✓

15001	\[ {}y^{\prime } = \frac {2+\sqrt {x}}{2+\sqrt {y}} \]	[_separable]	✓

15002	\[ {}y^{\prime }-3 x^{2} y^{2} = -3 x^{2} \]	[_separable]	✓

15003	\[ {}y^{\prime }-3 x^{2} y^{2} = 3 x^{2} \]	[_separable]	✓

15006	\[ {}y y^{\prime } = \sin \left (x \right ) \] i.c.	[_separable]	✓

15007	\[ {}y^{\prime } = 2 x -1+2 x y-y \] i.c.	[_separable]	✓

15008	\[ {}y^{\prime } x = y^{2}-y \] i.c.	[_separable]	✓

15009	\[ {}y^{\prime } x = y^{2}-y \] i.c.	[_separable]	✓

15010	\[ {}y^{\prime } = \frac {-1+y^{2}}{x y} \] i.c.	[_separable]	✓

15011	\[ {}\left (-1+y^{2}\right ) y^{\prime } = 4 x y \] i.c.	[_separable]	✓

15019	\[ {}y^{\prime } = y \sin \left (x \right ) \]	[_separable]	✓

15025	\[ {}y^{\prime }-2 x y = x \]	[_separable]	✓

15073	\[ {}2-2 x +3 y^{2} y^{\prime } = 0 \]	[_separable]	✓

15077	\[ {}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0 \]	[_separable]	✓

15079	\[ {}1+y^{4}+x y^{3} y^{\prime } = 0 \]	[_separable]	✓

15083	\[ {}3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime } = 0 \]	[_separable]	✓

15084	\[ {}2 x \left (1+y\right )-y^{\prime } = 0 \]	[_separable]	✓

15089	\[ {}y^{\prime } x = 2 y^{2}-6 y \]	[_separable]	✓

15090	\[ {}4 y^{2}-x^{2} y^{2}+y^{\prime } = 0 \]	[_separable]	✓

15104	\[ {}y^{\prime } = \frac {1}{x y-3 x} \]	[_separable]	✓

15107	\[ {}\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

15113	\[ {}y^{\prime } = x y^{2}+3 y^{2}+x +3 \]	[_separable]	✓

15127	\[ {}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0 \]	[_separable]	✓

15130	\[ {}y^{\prime } = y^{3}-y^{3} \cos \left (x \right ) \]	[_separable]	✓

15132	\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \]	[_separable]	✓

15134	\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \]	[_separable]	✓

15720	\[ {}y^{\prime }+x y = 0 \]	[_separable]	✓

15731	\[ {}y^{\prime } = -\frac {x}{y} \]	[_separable]	✓

15761	\[ {}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (-2+y\right )} \]	[_separable]	✓

15771	\[ {}y^{\prime }+\cos \left (x \right ) y = 0 \]	[_separable]	✓

15794	\[ {}\frac {y^{\prime }}{t} = \sqrt {y} \] i.c.	[_separable]	✓

15796	\[ {}y^{\prime } = y \sqrt {t} \] i.c.	[_separable]	✓

15798	\[ {}y^{\prime } t = y \]	[_separable]	✓

15799	\[ {}y^{\prime } = \tan \left (t \right ) y \] i.c.	[_separable]	✓

15820	\[ {}y^{\prime } = t y^{2} \] i.c.	[_separable]	✓

15821	\[ {}y^{\prime } = -\frac {t}{y} \] i.c.	[_separable]	✓

15823	\[ {}y^{\prime } = \frac {x}{y^{2}} \]	[_separable]	✓

15824	\[ {}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0 \]	[_separable]	✓

15825	\[ {}y^{\prime } = \frac {\sqrt {y}}{x^{2}} \]	[_separable]	✓

15827	\[ {}6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime } = 0 \]	[_separable]	✓

15828	\[ {}\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime } = 0 \]	[_separable]	✓

15829	\[ {}4 \sinh \left (4 y\right ) y^{\prime } = 6 \cosh \left (3 x \right ) \]	[_separable]	✓

15830	\[ {}y^{\prime } = \frac {1+y}{1+t} \]	[_separable]	✓

15831	\[ {}y^{\prime } = \frac {y+2}{2 t +1} \]	[_separable]	✓

15832	\[ {}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \]	[_separable]	✓

15833	\[ {}3 \sin \left (x \right )-4 y^{\prime } \cos \left (y\right ) = 0 \]	[_separable]	✓

15834	\[ {}\cos \left (y\right ) y^{\prime } = 8 \sin \left (8 t \right ) \]	[_separable]	✓

15836	\[ {}\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right ) = 0 \]	[_separable]	✓

15837	\[ {}\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

15838	\[ {}y^{\prime } = {\mathrm e}^{2 y+10 t} \]	[_separable]	✓

15839	\[ {}y^{\prime } = {\mathrm e}^{3 y+2 t} \]	[_separable]	✓

15840	\[ {}\sin \left (t \right )^{2} = \cos \left (y\right )^{2} y^{\prime } \]	[_separable]	✓

15841	\[ {}3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime } \]	[_separable]	✓

15842	\[ {}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \]	[_separable]	✓

15843	\[ {}\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2} = 0 \]	[_separable]	✓

15845	\[ {}\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right ) = 0 \]	[_separable]	✓

15846	\[ {}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \]	[_separable]	✓

15847	\[ {}x \sin \left (x^{2}\right ) = \frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \]	[_separable]	✓

15848	\[ {}\frac {x -2}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \]	[_separable]	✓

15849	\[ {}\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}} = \sin \left (x \right )^{3} \cos \left (x \right ) \]	[_separable]	✓

15850	\[ {}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \]	[_separable]	✓

15851	\[ {}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \]	[_separable]	✓

15852	\[ {}y^{\prime } = \frac {5^{-t}}{y^{2}} \]	[_separable]	✓

15853	\[ {}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1 \]	[_separable]	✓

15855	\[ {}4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0 \]	[_separable]	✓

15856	\[ {}y^{\prime } = \sin \left (t -y\right )+\sin \left (t +y\right ) \]	[_separable]	✓

15867	\[ {}y^{\prime } = \frac {\sqrt {t}}{y} \] i.c.	[_separable]	✓

15869	\[ {}y^{\prime } = \frac {{\mathrm e}^{t}}{1+y} \] i.c.	[_separable]	✓

15870	\[ {}y^{\prime } = {\mathrm e}^{t -y} \] i.c.	[_separable]	✓

15874	\[ {}y^{\prime } = \frac {\sin \left (x \right )}{\cos \left (y\right )+1} \] i.c.	[_separable]	✓

15875	\[ {}y^{\prime } = \frac {3+y}{3 x +1} \] i.c.	[_separable]	✓

15876	\[ {}y^{\prime } = {\mathrm e}^{x -y} \] i.c.	[_separable]	✓

15877	\[ {}y^{\prime } = {\mathrm e}^{2 x -y} \] i.c.	[_separable]	✓

15878	\[ {}y^{\prime } = \frac {3 y+1}{3+x} \] i.c.	[_separable]	✓

15879	\[ {}y^{\prime } = \cos \left (t \right ) y \] i.c.	[_separable]	✓

15880	\[ {}y^{\prime } = y^{2} \cos \left (t \right ) \] i.c.	[_separable]	✓

15881	\[ {}y^{\prime } = \sqrt {y}\, \cos \left (t \right ) \] i.c.	[_separable]	✓

15882	\[ {}y^{\prime }+y f \left (t \right ) = 0 \] i.c.	[_separable]	✓

15883	\[ {}y^{\prime } = -\frac {-2+y}{x -2} \] i.c.	[_separable]	✓

15893	\[ {}y^{\prime } = y f \left (t \right ) \] i.c.	[_separable]	✓

15912	\[ {}y^{\prime }-x y = x \]	[_separable]	✓

15916	\[ {}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1} \]	[_separable]	✓

15922	\[ {}2 t y+y^{\prime } = 2 t \] i.c.	[_separable]	✓

15926	\[ {}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t \] i.c.	[_separable]	✓

15954	\[ {}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0 \]	[_separable]	✓

15955	\[ {}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0 \]	[_separable]	✓

15957	\[ {}3 t y^{2}+y^{3} y^{\prime } = 0 \]	[_separable]	✓

15961	\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \]	[_separable]	✓

15964	\[ {}y^{2}+2 t y y^{\prime } = 0 \]	[_separable]	✓

15965	\[ {}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0 \]	[_separable]	✓

15970	\[ {}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0 \]	[_separable]	✓

15974	\[ {}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0 \]	[_separable]	✓

15982	\[ {}2 t y^{2}+2 t^{2} y y^{\prime } = 0 \] i.c.	[_separable]	✓

15994	\[ {}t^{2} y+t^{3} y^{\prime } = 0 \]	[_separable]	✓

15995	\[ {}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0 \]	[_separable]	✓

16015	\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \]	[_separable]	✓

16019	\[ {}2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime } = 0 \]	[_separable]	✓

16021	\[ {}\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )} = 0 \]	[_separable]	✓

16022	\[ {}\sqrt {t^{2}+1}+y y^{\prime } = 0 \]	[_separable]	✓

16052	\[ {}y^{\prime }-\frac {2 y}{x} = -x^{2} y \]	[_separable]	✓

16066	\[ {}y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \]	[_separable]	✓

16067	\[ {}\cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right ) = 0 \]	[_separable]	✓

16068	\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \]	[_separable]	✓

16069	\[ {}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t} \]	[_separable]	✓

16070	\[ {}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \]	[_separable]	✓

16071	\[ {}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime } \]	[_separable]	✓

16072	\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \]	[_separable]	✓

16073	\[ {}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \]	[_separable]	✓

16086	\[ {}t y+y^{\prime } = t \]	[_separable]	✓

16103	\[ {}y^{\prime } = t y^{3} \] i.c.	[_separable]	✓

16104	\[ {}y^{\prime } = \frac {t}{y^{3}} \] i.c.	[_separable]	✓

16105	\[ {}y^{\prime } = -\frac {y}{t -2} \] i.c.	[_separable]	✓

16594	\[ {}y^{\prime } = \frac {x}{y} \]	[_separable]	✓

16606	\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = 2 x \]	[_separable]	✓

16612	\[ {}y^{\prime } = x \left (-1+y\right ) \]	[_separable]	✓

16617	\[ {}y^{\prime } = \frac {1+y}{x -1} \]	[_separable]	✓

16622	\[ {}y^{\prime } = -\frac {y}{x} \]	[_separable]	✓

16632	\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]	[_separable]	✓

16633	\[ {}x y^{\prime } y+1+y^{2} = 0 \]	[_separable]	✓

16634	\[ {}y^{\prime } \sin \left (x \right )-\cos \left (x \right ) y = 0 \] i.c.	[_separable]	✓

16635	\[ {}1+y^{2} = y^{\prime } x \]	[_separable]	✓

16636	\[ {}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0 \]	[_separable]	✓

16637	\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \] i.c.	[_separable]	✓

16639	\[ {}y \ln \left (y\right )+y^{\prime } x = 1 \] i.c.	[_separable]	✓

16640	\[ {}y^{\prime } = a^{x +y} \]	[_separable]	✓

16641	\[ {}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0 \]	[_separable]	✓

16642	\[ {}2 x \sqrt {1-y^{2}} = \left (x^{2}+1\right ) y^{\prime } \]	[_separable]	✓

16643	\[ {}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left ({\mathrm e}^{2 x}+1\right ) \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

16644	\[ {}\sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

16649	\[ {}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0 \] i.c.	[_separable]	✓

16650	\[ {}y^{\prime } = \frac {y}{x} \] i.c.	[_separable]	✓

16660	\[ {}x^{3} y^{\prime }-\sin \left (y\right ) = 1 \] i.c.	[_separable]	✓

16661	\[ {}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0 \] i.c.	[_separable]	✓

16663	\[ {}\left (x +1\right ) y^{\prime } = -1+y \]	[_separable]	✓

16664	\[ {}y^{\prime } = 2 x \left (\pi +y\right ) \]	[_separable]	✓

16695	\[ {}y^{\prime }+\cos \left (x \right ) y = \cos \left (x \right ) \] i.c.	[_separable]	✓

16709	\[ {}y^{\prime }+2 x y = 2 x y^{2} \]	[_separable]	✓

16712	\[ {}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}} \]	[_separable]	✓

16717	\[ {}y^{\prime }-\cos \left (x \right ) y = y^{2} \cos \left (x \right ) \]	[_separable]	✓

16730	\[ {}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0 \]	[_separable]	✓

16747	\[ {}{y^{\prime }}^{2}-2 y y^{\prime } = y^{2} \left (-1+{\mathrm e}^{2 x}\right ) \]	[_separable]	✓

16810	\[ {}y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right ) = \cos \left (\frac {x}{2}-\frac {y}{2}\right ) \]	[_separable]	✓

16811	\[ {}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0 \]	[_separable]	✓

16818	\[ {}\left (x -1\right ) \left (y^{2}-y+1\right ) = \left (-1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \]	[_separable]	✓

16827	\[ {}\sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime } = 0 \]	[_separable]	✓

16854	\[ {}x y = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \]	[_separable]	✓

17229	\[ {}y^{\prime } = \frac {x^{4}}{y} \]	[_separable]	✓

17230	\[ {}y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y} \]	[_separable]	✓

17231	\[ {}y^{\prime }+y^{3} \sin \left (x \right ) = 0 \]	[_separable]	✓

17232	\[ {}y^{\prime } = \frac {7 x^{2}-1}{7+5 y} \]	[_separable]	✓

17233	\[ {}y^{\prime } = \sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \]	[_separable]	✓

17234	\[ {}y^{\prime } x = \sqrt {1-y^{2}} \]	[_separable]	✓

17235	\[ {}y y^{\prime } = \left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \]	[_separable]	✓

17236	\[ {}y^{\prime } = \frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \]	[_separable]	✓

17237	\[ {}y^{\prime } = \frac {x^{2}}{1+y^{2}} \]	[_separable]	✓

17238	\[ {}y^{\prime } = \frac {\sec \left (x \right )^{2}}{y^{3}+1} \]	[_separable]	✓

17240	\[ {}y^{\prime } = x \left (y-y^{2}\right ) \]	[_separable]	✓

17241	\[ {}y^{\prime } = \left (1-12 x \right ) y^{2} \] i.c.	[_separable]	✓

17242	\[ {}y^{\prime } = \frac {3-2 x}{y} \] i.c.	[_separable]	✓

17243	\[ {}x +y y^{\prime } {\mathrm e}^{-x} = 0 \] i.c.	[_separable]	✓

17244	\[ {}r^{\prime } = \frac {r^{2}}{\theta } \] i.c.	[_separable]	✓

17245	\[ {}y^{\prime } = \frac {3 x}{y+x^{2} y} \] i.c.	[_separable]	✓

17246	\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] i.c.	[_separable]	✓

17247	\[ {}y^{\prime } = 2 x y^{2}+4 x^{3} y^{2} \] i.c.	[_separable]	✓

17248	\[ {}y^{\prime } = x^{2} {\mathrm e}^{-3 y} \] i.c.	[_separable]	✓

17249	\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right ) \] i.c.	[_separable]	✓

17250	\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6} \] i.c.	[_separable]	✓

17251	\[ {}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \] i.c.	[_separable]	✓

17252	\[ {}x^{2} y^{\prime } = y-x y \] i.c.	[_separable]	✓

17253	\[ {}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \] i.c.	[_separable]	✓

17254	\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-4}} \] i.c.	[_separable]	✓

17255	\[ {}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

17256	\[ {}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right ) \] i.c.	[_separable]	✓

17257	\[ {}y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y} \] i.c.	[_separable]	✓

17258	\[ {}y^{\prime } = \frac {2 x^{2}}{2 y^{2}-6} \] i.c.	[_separable]	✓

17259	\[ {}y^{\prime } = 2 y^{2}+x y^{2} \] i.c.	[_separable]	✓

17260	\[ {}y^{\prime } = \frac {6-{\mathrm e}^{x}}{3+2 y} \] i.c.	[_separable]	✓

17261	\[ {}y^{\prime } = \frac {2 \cos \left (2 x \right )}{10+2 y} \] i.c.	[_separable]	✓

17262	\[ {}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right ) \] i.c.	[_separable]	✓

17263	\[ {}y^{\prime } = \frac {t \left (4-y\right ) y}{3} \] i.c.	[_separable]	✓

17264	\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{1+t} \] i.c.	[_separable]	✓

17302	\[ {}y+\left (t -4\right ) t y^{\prime } = 0 \] i.c.	[_separable]	✓

17311	\[ {}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \]	[_separable]	✓

17312	\[ {}y^{\prime } = \frac {\cot \left (t \right ) y}{1+y} \]	[_separable]	✓

17315	\[ {}y^{\prime } = -\frac {4 t}{y} \] i.c.	[_separable]	✓

17316	\[ {}y^{\prime } = 2 t y^{2} \] i.c.	[_separable]	✓

17318	\[ {}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y} \] i.c.	[_separable]	✓

17319	\[ {}y^{\prime } = t \left (3-y\right ) y \]	[_separable]	✓

17323	\[ {}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0 \] i.c.	[_separable]	✓

17324	\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \]	[_separable]	✓

17327	\[ {}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

17334	\[ {}\ln \left (y\right ) x +x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \]	[_separable]	✓

17335	\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]	[_separable]	✓

17338	\[ {}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0 \]	[_separable]	✓

17341	\[ {}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

17350	\[ {}y y^{\prime } = x +1 \]	[_separable]	✓

17351	\[ {}\left (1+y^{4}\right ) y^{\prime } = x^{4}+1 \]	[_separable]	✓

17353	\[ {}x \left (x -1\right ) y^{\prime } = y \left (1+y\right ) \]	[_separable]	✓

17366	\[ {}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right ) \]	[_separable]	✓

17377	\[ {}\frac {\sqrt {x}\, y^{\prime }}{y} = 1 \]	[_separable]	✓

17378	\[ {}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0 \]	[_separable]	✓

17823	\[ {}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0 \] i.c.	[_separable]	✓

17824	\[ {}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

17825	\[ {}y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0 \]	[_separable]	✓

17865	\[ {}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0 \]	[_quadrature]	✓

17867	\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0 \]	[_quadrature]	✓

17986	\[ {}y^{\prime } x = 2 y \]	[_separable]	✓

17987	\[ {}y y^{\prime } = {\mathrm e}^{2 x} \]	[_separable]	✓

18007	\[ {}x y^{\prime } y = -1+y \]	[_separable]	✓

18008	\[ {}x^{5} y^{\prime }+y^{5} = 0 \]	[_separable]	✓

18009	\[ {}y^{\prime } x = \left (-2 x^{2}+1\right ) \tan \left (y\right ) \]	[_separable]	✓

18010	\[ {}y^{\prime } = 2 x y \]	[_separable]	✓

18011	\[ {}y^{\prime } \sin \left (y\right ) = x^{2} \]	[_separable]	✓

18013	\[ {}y^{\prime }+y \tan \left (x \right ) = 0 \]	[_separable]	✓

18014	\[ {}y^{\prime }-y \tan \left (x \right ) = 0 \]	[_separable]	✓

18015	\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]	[_separable]	✓

18016	\[ {}y \ln \left (y\right )-y^{\prime } x = 0 \]	[_separable]	✓

18023	\[ {}y^{\prime } = {\mathrm e}^{3 x -2 y} \] i.c.	[_separable]	✓

18025	\[ {}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

18026	\[ {}3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime } = 0 \] i.c.	[_separable]	✓

18028	\[ {}x y^{\prime } y = \left (x +1\right ) \left (1+y\right ) \] i.c.	[_separable]	✓

18056	\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]	[_separable]	✓

18057	\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

18059	\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \]	[_separable]	✓

18060	\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \]	[_separable]	✓

18066	\[ {}\ln \left (y\right ) x +x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \]	[_separable]	✓

18069	\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]	[_separable]	✓

18077	\[ {}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

18085	\[ {}y-y^{\prime } x = x y^{3} y^{\prime } \]	[_separable]	✓

18089	\[ {}y^{\prime } x -y+y^{2} = 0 \]	[_separable]	✓

18135	\[ {}y^{\prime } x +y = x^{2} y^{\prime }+y^{2} \]	[_separable]	✓

18158	\[ {}3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y} = 0 \]	[_separable]	✓

18429	\[ {}3 x t^{2}-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime } = 0 \]	[_separable]	✓

18430	\[ {}1+2 x+\left (-t^{2}+4\right ) x^{\prime } = 0 \]	[_separable]	✓

18436	\[ {}x^{\prime }+x \tan \left (t \right ) = 0 \]	[_separable]	✓

18439	\[ {}x^{\prime }+2 t x+t x^{4} = 0 \]	[_separable]	✓

18464	\[ {}y^{\prime } = \frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \]	[_separable]	✓

18469	\[ {}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0 \]	[_separable]	✓

18471	\[ {}y-y^{\prime } x = b \left (1+x^{2} y^{\prime }\right ) \]	[_separable]	✓

18473	\[ {}y^{\prime } = 1+\frac {1}{x}-\frac {1}{y^{2}+2}-\frac {1}{x \left (y^{2}+2\right )} \]	[_separable]	✓

18477	\[ {}\sec \left (x \right )^{2} \tan \left (y\right ) y^{\prime }+\sec \left (y\right )^{2} \tan \left (x \right ) = 0 \]	[_separable]	✓

18481	\[ {}y^{\prime }+x y = x \]	[_separable]	✓

18498	\[ {}y^{\prime } = x \left (a y^{2}+b \right ) \]	[_separable]	✓

18499	\[ {}n^{\prime } = \left (n^{2}+1\right ) x \]	[_separable]	✓

18500	\[ {}v^{\prime }+\frac {2 v}{u} = 3 v \]	[_separable]	✓

18501	\[ {}\sqrt {-u^{2}+1}\, v^{\prime } = 2 u \sqrt {1-v^{2}} \]	[_separable]	✓

18503	\[ {}\frac {y^{\prime }}{x} = y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \]	[_separable]	✓

18505	\[ {}v^{\prime }+2 u v = 2 u \]	[_separable]	✓

18506	\[ {}1+v^{2}+\left (u^{2}+1\right ) v v^{\prime } = 0 \]	[_separable]	✓

18507	\[ {}u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2} = 1 \]	[_separable]	✓

18556	\[ {}y^{\prime }+y \sin \left (x \right ) = \sin \left (x \right ) y^{2} \]	[_separable]	✓

18557	\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \]	[_separable]	✓

18561	\[ {}y \sqrt {x^{2}-1}+x \sqrt {-1+y^{2}}\, y^{\prime } = 0 \]	[_separable]	✓

18562	\[ {}\left (1+{\mathrm e}^{y}\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

18563	\[ {}\sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

18564	\[ {}y \left (3+y\right ) y^{\prime } = x \left (3+2 y\right ) \]	[_separable]	✓

18567	\[ {}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \]	[_separable]	✓

18656	\[ {}\left (1-x \right ) y^{\prime }-1-y = 0 \]	[_separable]	✓

18658	\[ {}y-y^{\prime } x = a \left (y^{\prime }+y^{2}\right ) \]	[_separable]	✓

18659	\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]	[_separable]	✓

18673	\[ {}a \left (y^{\prime } x +2 y\right ) = x y^{\prime } y \]	[_separable]	✓

18698	\[ {}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

18699	\[ {}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

18712	\[ {}\left (x +1\right ) y^{\prime }+1 = 2 \,{\mathrm e}^{y} \]	[_separable]	✓

18718	\[ {}y y^{\prime } = a x \]	[_separable]	✓

18723	\[ {}y-y^{\prime } x = b \left (1+x^{2} y^{\prime }\right ) \]	[_separable]	✓

18734	\[ {}4 y^{2} {y^{\prime }}^{2}+2 \left (3 x +1\right ) x y y^{\prime }+3 x^{3} = 0 \]	[_separable]	✓

18750	\[ {}x y \left (y-y^{\prime } x \right ) = y y^{\prime }+x \]	[_separable]	✓

18765	\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2} \]	[_separable]	✓

18770	\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0 \]	[_quadrature]	✓

18779	\[ {}\sqrt {x}\, y^{\prime } = \sqrt {y} \]	[_separable]	✓

18986	\[ {}x \cos \left (y\right )^{2} = y \cos \left (x \right )^{2} y^{\prime } \]	[_separable]	✓

18987	\[ {}y^{\prime } = {\mathrm e}^{x -y}+x^{2} {\mathrm e}^{-y} \]	[_separable]	✓

18988	\[ {}x^{2} y^{\prime }+y = 1 \]	[_separable]	✓

18989	\[ {}2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

18990	\[ {}x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

18991	\[ {}y^{\prime } = {\mathrm e}^{x +y}+x^{2} {\mathrm e}^{y} \]	[_separable]	✓

18992	\[ {}\left (3+2 \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime } = 1+2 \sin \left (y\right )+\cos \left (y\right ) \]	[_separable]	✓

18993	\[ {}\frac {\cos \left (y\right )^{2} y^{\prime }}{x}+\frac {\cos \left (x \right )^{2}}{y} = 0 \]	[_separable]	✓

18994	\[ {}\left ({\mathrm e}^{x}+1\right ) y y^{\prime } = \left (1+y\right ) {\mathrm e}^{x} \]	[_separable]	✓

18995	\[ {}\csc \left (x \right ) \ln \left (y\right ) y^{\prime }+x^{2} y^{2} = 0 \]	[_separable]	✓

18996	\[ {}y^{\prime } = \frac {\sin \left (x \right )+x \cos \left (x \right )}{y \left (2 \ln \left (y\right )+1\right )} \]	[_separable]	✓

18997	\[ {}\cos \left (y\right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right ) = \cos \left (x \right ) \ln \left (\sec \left (y\right )+\tan \left (y\right )\right ) y^{\prime } \]	[_separable]	✓

18998	\[ {}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \]	[_separable]	✓

18999	\[ {}\left (\sin \left (y\right )+y \cos \left (y\right )\right ) y^{\prime }-\left (2 \ln \left (x \right )+1\right ) x = 0 \]	[_separable]	✓

19000	\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]	[_separable]	✓

19001	\[ {}y-y^{\prime } x = a \left (y^{\prime }+y^{2}\right ) \]	[_separable]	✓

19042	\[ {}x +y^{\prime } = x \,{\mathrm e}^{\left (n -1\right ) y} \]	[_separable]	✓

19071	\[ {}y^{\prime } = {\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \]	[_separable]	✓

19076	\[ {}y^{\prime } = \frac {x \left (2 \ln \left (x \right )+1\right )}{\sin \left (y\right )+y \cos \left (y\right )} \]	[_separable]	✓

19077	\[ {}s^{\prime }+x^{2} = x^{2} {\mathrm e}^{3 s} \]	[_separable]	✓

19144	\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2} \]	[_separable]	✓

19147	\[ {}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0 \]	[_quadrature]	✓

19149	\[ {}x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y = 0 \]	[_quadrature]	✓

19170	\[ {}x = y+a \ln \left (y^{\prime }\right ) \]	[_separable]	✓

19239	\[ {}4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2} = 0 \]	[_separable]	✓

19241	\[ {}y-y^{\prime } x = a \left (y^{\prime }+y^{2}\right ) \]	[_separable]	✓

19242	\[ {}y-y^{\prime } x = b \left (1+x^{2} y^{\prime }\right ) \]	[_separable]	✓

19438	\[ {}y-y^{\prime } x = 0 \]	[_separable]	✓

19439	\[ {}\cot \left (y\right )-y^{\prime } \tan \left (x \right ) = 0 \]	[_separable]	✓

19442	\[ {}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0 \]	[_separable]	✓

19443	\[ {}1+y^{2}-x y^{\prime } y = 0 \]	[_separable]	✓

19473	\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0 \]	[_quadrature]	✓

19489	\[ {}x y \left (y-y^{\prime } x \right ) = y y^{\prime }+x \]	[_separable]	✓

2.3.2 ﬁrst order ode separable