Problems 1 to 100

Table 2.3: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

1	$y^{'} = 2 x + 1$ i.c.	[_quadrature]	✓	0.472

2	$y^{'} = {(x - 2)}^{2}$ i.c.	[_quadrature]	✓	0.636

3	$y^{'} = \sqrt{x}$ i.c.	[_quadrature]	✓	0.617

4	$y^{'} = \frac{1}{x^{2}}$ i.c.	[_quadrature]	✓	0.609

5	$y^{'} = \frac{1}{\sqrt{x + 2}}$ i.c.	[_quadrature]	✓	0.651

6	$y^{'} = x \sqrt{x^{2} + 9}$ i.c.	[_quadrature]	✓	0.907

7	$y^{'} = \frac{10}{x^{2} + 1}$ i.c.	[_quadrature]	✓	0.634

8	$y^{'} = \cos (2 x)$ i.c.	[_quadrature]	✓	0.714

9	$y^{'} = \frac{1}{\sqrt{- x^{2} + 1}}$ i.c.	[_quadrature]	✓	0.673

10	$y^{'} = x e^{- x}$ i.c.	[_quadrature]	✓	0.639

11	$x^{''} = 50$ i.c.	[[_2nd_order, _quadrature]]	✓	1.167

12	$x^{''} = - 20$ i.c.	[[_2nd_order, _quadrature]]	✓	1.168

13	$x^{''} = 3 t$ i.c.	[[_2nd_order, _quadrature]]	✓	1.253

14	$x^{''} = 2 t + 1$ i.c.	[[_2nd_order, _quadrature]]	✓	2.791

15	$x^{''} = 4 {(t + 3)}^{2}$ i.c.	[[_2nd_order, _quadrature]]	✓	2.979

16	$x^{''} = \frac{1}{\sqrt{t + 4}}$ i.c.	[[_2nd_order, _quadrature]]	✓	3.240

17	$x^{''} = \frac{1}{{(1 + t)}^{3}}$ i.c.	[[_2nd_order, _quadrature]]	✓	1.448

18	$x^{''} = 50 \sin (5 t)$ i.c.	[[_2nd_order, _quadrature]]	✓	3.940

19	$y^{'} = - y - \sin (x)$	[[_linear, ‘class A‘]]	✓	1.481

20	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓	0.988

21	$y^{'} = y - \sin (x)$	[[_linear, ‘class A‘]]	✓	1.427

22	$y^{'} = x - y$	[[_linear, ‘class A‘]]	✓	1.033

23	$y^{'} = y - x + 1$	[[_linear, ‘class A‘]]	✓	1.235

24	$y^{'} = x - y + 1$	[[_linear, ‘class A‘]]	✓	1.211

25	$y^{'} = x^{2} - y$	[[_linear, ‘class A‘]]	✓	1.035

26	$y^{'} = x^{2} - y - 2$	[[_linear, ‘class A‘]]	✓	0.996

27	$y^{'} = 2 x^{2} y^{2}$ i.c.	[_separable]	✓	2.248

28	$y^{'} = \ln (y) x$ i.c.	[_separable]	✓	2.376

29	$y^{'} = y^{1 / 3}$ i.c.	[_quadrature]	✓	1.492

30	$y^{'} = y^{1 / 3}$ i.c.	[_quadrature]	✓	1.295

31	$y^{'} = \sqrt{x - y}$ i.c.	[[_homogeneous, ‘class C‘], _dAlembert]	✓	4.374

32	$y^{'} = \sqrt{x - y}$ i.c.	[[_homogeneous, ‘class C‘], _dAlembert]	✓	5.260

33	$y y^{'} = x - 1$ i.c.	[_separable]	✓	4.604

34	$y y^{'} = x - 1$ i.c.	[_separable]	✓	5.933

35	$y^{'} = \ln (1 + y^{2})$ i.c.	[_quadrature]	✓	2.252

36	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✗	2.144

37	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓	1.292

38	$y^{'} = y - x$ i.c.	[[_linear, ‘class A‘]]	✓	1.410

39	$y^{'} = x^{2} + y^{2} - 1$ i.c.	[_Riccati]	✓	4.494

40	$y^{'} = x + \frac{y^{2}}{2}$ i.c.	[[_Riccati, _special]]	✓	2.226

41	$y^{'} + 2 x y = 0$	[_separable]	✓	1.152

42	$y^{'} + 2 x y^{2} = 0$	[_separable]	✓	1.673

43	$y^{'} = y \sin (x)$	[_separable]	✓	1.562

44	$(x + 1) y^{'} = 4 y$	[_separable]	✓	1.555

45	$2 \sqrt{x} y^{'} = \sqrt{1 - y^{2}}$	[_separable]	✓	1.637

46	$y^{'} = 3 \sqrt{x y}$	[[_homogeneous, ‘class G‘]]	✓	8.087

47	$y^{'} = 64^{1 / 3} {(x y)}^{1 / 3}$	[[_homogeneous, ‘class G‘]]	✓	5.340

48	$y^{'} = 2 x \sec (y)$	[_separable]	✓	1.479

49	$(- x^{2} + 1) y^{'} = 2 y$	[_separable]	✓	1.413

50	${(x + 1)}^{2} y^{'} = {(1 + y)}^{2}$	[_separable]	✓	2.075

51	$y^{'} = x y^{3}$	[_separable]	✓	3.287

52	$y y^{'} = x (1 + y^{2})$	[_separable]	✓	2.088

53	$y^{3} y^{'} = (1 + y^{4}) \cos (x)$	[_separable]	✓	4.984

54	$y^{'} = \frac{1 + \sqrt{x}}{1 + \sqrt{y}}$	[_separable]	✓	1.690

55	$y^{'} = \frac{(x - 1) y^{5}}{x^{2} (2 y^{3} - y)}$	[_separable]	✓	1.969

56	$(x^{2} + 1) \tan (y) y^{'} = x$	[_separable]	✓	1.984

57	$y^{'} = 1 + x + y + x y$	[_separable]	✓	1.236

58	$x^{2} y^{'} = 1 - x^{2} + y^{2} - x^{2} y^{2}$	[_separable]	✓	3.015

59	$y^{'} = y e^{x}$ i.c.	[_separable]	✓	2.595

60	$y^{'} = 3 x^{2} (1 + y^{2})$ i.c.	[_separable]	✓	2.727

61	$2 y y^{'} = \frac{x}{\sqrt{x^{2} - 16}}$ i.c.	[_separable]	✓	2.611

62	$y^{'} = 4 x^{3} y - y$ i.c.	[_separable]	✓	1.914

63	$y^{'} + 1 = 2 y$ i.c.	[_quadrature]	✓	1.057

64	$y^{'} \tan (x) = y$ i.c.	[_separable]	✓	1.930

65	$y^{'} x - y = 2 x^{2} y$ i.c.	[_separable]	✓	1.688

66	$y^{'} = 2 x y^{2} + 3 x^{2} y^{2}$ i.c.	[_separable]	✓	1.897

67	$y^{'} = 6 e^{2 x - y}$ i.c.	[_separable]	✓	2.489

68	$2 \sqrt{x} y^{'} = \cos {(y)}^{2}$ i.c.	[_separable]	✓	2.174

69	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.643

70	${y^{'}}^{2} = 4 y$ i.c.	[_quadrature]	✓	0.548

71	$y^{'} = 2 \sqrt{y}$ i.c.	[_quadrature]	✓	4.204

72	$y^{'} = y \sqrt{- 1 + y^{2}}$ i.c.	[_quadrature]	✓	71.745

73	$y^{'} + y = 2$ i.c.	[_quadrature]	✓	0.983

74	$y^{'} - 2 y = 3 e^{2 x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.279

75	$y^{'} + 3 y = 2 x e^{- 3 x}$	[[_linear, ‘class A‘]]	✓	1.670

76	$y^{'} - 2 x y = e^{x^{2}}$	[_linear]	✓	1.407

77	$y^{'} x + 2 y = 3 x$ i.c.	[_linear]	✓	2.577

78	$y^{'} x + 5 y = 7 x^{2}$ i.c.	[_linear]	✓	1.704

79	$2 y^{'} x + y = 10 \sqrt{x}$	[_linear]	✓	3.974

80	$3 y^{'} x + y = 12 x$	[_linear]	✓	1.811

81	$y^{'} x - y = x$ i.c.	[_linear]	✓	1.656

82	$2 y^{'} x - 3 y = 9 x^{3}$	[_linear]	✓	1.505

83	$y^{'} x + y = 3 x y$ i.c.	[_separable]	✓	2.278

84	$y^{'} x + 3 y = 2 x^{5}$ i.c.	[_linear]	✓	1.848

85	$y^{'} + y = e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.284

86	$y^{'} x - 3 y = x^{3}$ i.c.	[_linear]	✓	1.350

87	$y^{'} + 2 x y = x$ i.c.	[_separable]	✓	1.466

88	$y^{'} = (1 - y) \cos (x)$ i.c.	[_separable]	✓	1.842

89	$(x + 1) y^{'} + y = \cos (x)$ i.c.	[_linear]	✓	1.897

90	$y^{'} x = 2 y + x^{3} \cos (x)$	[_linear]	✓	1.628

91	$y^{'} + \cot (x) y = \cos (x)$	[_linear]	✓	1.990

92	$y^{'} = 1 + x + y + x y$ i.c.	[_separable]	✓	1.550

93	$y^{'} x = 3 y + x^{4} \cos (x)$ i.c.	[_linear]	✓	2.642

94	$y^{'} = 2 x y + 3 x^{2} e^{x^{2}}$ i.c.	[_linear]	✓	2.678

95	$y^{'} x + (2 x - 3) y = 4 x^{4}$	[_linear]	✓	2.430

96	$(x^{2} + 4) y^{'} + 3 x y = x$ i.c.	[_separable]	✓	1.998

97	$(x^{2} + 1) y^{'} + 3 x^{3} y = 6 x e^{- \frac{3 x^{2}}{2}}$ i.c.	[_linear]	✓	2.337

98	$\frac{1 - 4 x y^{2}}{x^{'}} = y^{3}$	[_linear]	✓	1.484

99	$\frac{x + y e^{y}}{x^{'}} = 1$	[[_linear, ‘class A‘]]	✓	1.399

100	$\frac{1 + 2 x y}{x^{'}} = y^{2} + 1$	[_linear]	✓	1.317

2.2.1 Problems 1 to 100