1.1 section 1

TableĀ 1.1: Lookup table

ID

problem

ODE

8585

1

\(\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

8586

2

\(\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0\)

8587

3

\(\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0\)

8588

4

\(\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0\)

8589

5

\(3 y^{\prime \prime }+y^{\prime } x -4 y = 0\)

8590

6

\(5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0\)

8591

7

\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\)

8592

8

\(\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\)

8593

9

\(y^{\prime \prime }+y^{\prime } x -2 y = 0\)

8594

10

\(\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0\)

8595

11

\(\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0\)

8596

12

\(t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y = 0\)

8597

13

\(t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0\)

8598

14

\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\)

8599

15

\(\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0\)

8600

16

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

8601

17

\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\)

8602

18

\(\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0\)

8603

19

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

8604

20

\(\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0\)

8605

21

\(\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\)

8606

22

\(2 y^{\prime \prime }+y^{\prime } x +3 y = 0\)

8607

23

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

8608

24

\(\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\)

8609

25

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

8610

26

\(\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0\)

8611

27

\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\)

8612

28

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

8613

29

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

8614

31

\(\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0\)

8615

32

\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\)

8616

33

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\)

8617

34

\(\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0\)

8618

35

\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\)

8619

36

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

8620

38

\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\)

8621

39

\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y = 0\)

8622

40

\(x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y = 0\)

8623

41

\(x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0\)

8624

42

\(x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0\)

8625

43

\(x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = 0\)

8626

44

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

8627

45

\(4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0\)

8628

46

\(\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0\)

8629

47

\(\left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y = 0\)

8630

48

\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (2-x \right ) y = 0\)

8631

49

\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0\)

8632

50

\(x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0\)

8633

51

\(x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0\)

8634

52

\(\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y = 0\)

8635

53

\(\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\)

8636

54

\(\left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y = 0\)

8637

55

\(\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y = 0\)

8638

56

\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0\)

8639

57

\(\left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y = 0\)

8640

58

\(\left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y = 0\)

8641

59

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

8642

60

\(\left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y = 0\)

8643

61

\(\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y = 0\)

8644

62

\(y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0\)

8645

63

\(\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0\)

8646

64

\(\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0\)

8647

65

\(\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0\)

8648

66

\(\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0\)

8649

67

\(y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0\)

8650

68

\(\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0\)

8651

69

\(y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0\)

8652

70

\(\left (3 x +1\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0\)

8653

71

\(\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0\)

8654

72

\(\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0\)

8655

73

\(\left (4+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0\)

8656

74

\(\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0\)

8657

75

\(x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0\)

8658

76

\(\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0\)

8659

77

\(\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0\)

8660

78

\(y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0\)

8661

79

\(\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0\)

8662

80

\(y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y = 0\)

8663

81

\(2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0\)

8664

82

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\)

8665

83

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\)

8666

84

\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\)

8667

85

\(3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0\)

8668

86

\(12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0\)

8669

87

\(x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0\)

8670

88

\(18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0\)

8671

89

\(2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0\)

8672

90

\(2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y = 0\)

8673

91

\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0\)

8674

92

\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y = 0\)

8675

93

\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\)

8676

94

\(2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0\)

8677

95

\(x^{2} \left (4+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\)

8678

96

\(2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0\)

8679

97

\(6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y = 0\)

8680

98

\(x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0\)

8681

99

\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0\)

8682

100

\(x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0\)

8683

101

\(8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\)

8684

102

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0\)

8685

103

\(x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0\)

8686

104

\(4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0\)

8687

105

\(3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0\)

8688

106

\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0\)

8689

107

\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0\)

8690

108

\(2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0\)

8691

109

\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0\)

8692

110

\(2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0\)

8693

111

\(9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0\)

8694

112

\(6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0\)

8695

113

\(9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\)

8696

114

\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\)

8697

115

\(8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0\)

8698

116

\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\)

8699

117

\(6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0\)

8700

118

\(28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0\)

8701

119

\(8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0\)

8702

120

\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0\)

8703

121

\(3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\)

8704

122

\(4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0\)

8705

123

\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\)

8706

124

\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\)

8707

125

\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0\)

8708

126

\(x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\)

8709

127

\(4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0\)

8710

128

\(x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0\)

8711

129

\(9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0\)

8712

130

\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0\)

8713

131

\(16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0\)

8714

132

\(9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0\)

8715

133

\(36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0\)

8716

134

\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0\)

8717

135

\(x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\)

8718

136

\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0\)

8719

137

\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0\)

8720

138

\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0\)

8721

139

\(x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0\)

8722

140

\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0\)

8723

141

\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\)

8724

142

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0\)

8725

143

\(4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\)

8726

144

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0\)

8727

145

\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\)

8728

146

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0\)

8729

147

\(4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\)

8730

148

\(3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\)

8731

149

\(9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0\)

8732

150

\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\)

8733

151

\(x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y = 0\)

8734

152

\(x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0\)

8735

153

\(x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0\)

8736

154

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0\)

8737

155

\(9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0\)

8738

156

\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0\)

8739

157

\(4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0\)

8740

158

\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0\)

8741

159

\(9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0\)

8742

160

\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0\)

8743

161

\(16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0\)

8744

162

\(x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0\)

8745

163

\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0\)

8746

164

\(x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\)

8747

165

\(9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0\)

8748

166

\(2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0\)

8749

167

\(x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0\)

8750

168

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0\)

8751

169

\(x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 y x^{2} = 0\)

8752

170

\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\)

8753

171

\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0\)

8754

172

\(x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y = 0\)

8755

173

\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0\)

8756

174

\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0\)

8757

175

\(x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0\)

8758

176

\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0\)

8759

177

\(4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0\)

8760

178

\(3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0\)

8761

179

\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0\)

8762

180

\(x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0\)

8763

181

\(x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0\)

8764

182

\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0\)

8765

183

\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0\)

8766

184

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0\)

8767

185

\(x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0\)

8768

186

\(x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0\)

8769

187

\(x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0\)

8770

188

\(x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0\)

8771

189

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 y x^{2} = 0\)

8772

190

\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0\)

8773

191

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0\)

8774

192

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0\)

8775

193

\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0\)

8776

194

\(y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0\)

8777

195

\(y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0\)

8778

196

\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0\)

8779

197

\(\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0\)

8780

198

\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0\)

8781

199

\(\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0\)

8782

200

\(t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0\)

8783

201

\(y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0\)

8784

202

\(y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0\)

8785

204

\(2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0\)

8786

205

\(2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0\)

8787

206

\(2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0\)

8788

207

\(2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0\)

8789

208

\(t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0\)

8790

209

\(t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0\)

8791

210

\(t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0\)

8792

211

\(t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0\)

8793

212

\(t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0\)

8794

213

\(t y^{\prime \prime }+t y^{\prime }+2 y = 0\)

8795

214

\(t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0\)

8796

215

\(t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0\)

8797

216

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0\)

8798

217

\(\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y = 0\)

8799

218

\(4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0\)

8800

219

\(f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0\)

8801

220

\(z y^{\prime \prime }-2 y^{\prime }+y z = 0\)

8802

221

\(z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0\)

8803

222

\(y^{\prime \prime }+2 y^{\prime } x +4 y = 0\)

8804

223

\(y^{\prime \prime }+y^{\prime } x +3 y = 0\)

8805

224

\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\)

8806

225

\(\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y = 0\)

8807

226

\(\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0\)

8808

227

\(y^{\prime \prime }+y^{\prime } x +\left (x +2\right ) y = 0\)

8809

228

\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0\)

8810

229

\(4 y^{\prime \prime }+y^{\prime } x +4 y = 0\)

8811

230

\(y^{\prime \prime }+y^{\prime } x -4 y = 0\)

8812

231

\(4 x y^{\prime \prime }-y^{\prime } x +2 y = 0\)

8813

232

\(6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0\)

8814

233

\(3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y = 0\)

8815

234

\(2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0\)

8816

235

\(4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0\)

8817

236

\(x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0\)

8818

237

\(x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0\)

8819

238

\(x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0\)

8820

239

\(x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0\)

8821

240

\(x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0\)

8822

241

\(x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0\)

8823

242

\(x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0\)

8824

243

\(x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0\)

8825

244

\(x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0\)

8826

245

\(x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0\)

8827

246

\(x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0\)

8828

247

\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0\)

8829

248

\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (2+3 x \right ) y = 0\)

8830

249

\(x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0\)

8831

250

\(4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0\)

8832

251

\(x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0\)

8833

252

\(x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0\)

8834

253

\(4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0\)

8835

254

\(x^{2} y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (x +2\right ) y = 0\)

8836

255

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0\)

8837

256

\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\)

8838

257

\(2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0\)

8839

258

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

8840

259

\(x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0\)

8841

260

\(x^{4} y^{\prime \prime }+y^{\prime } x +y = 0\)

8842

261

\(x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0\)

8843

262

\(\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0\)

8844

263

\(x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0\)

8845

264

\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y = 0\)

8846

265

\(x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {y^{\prime } x}{2}-\frac {3 x y}{4} = 0\)

8847

266

\(x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0\)

8848

267

\(x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0\)

8849

268

\(x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0\)

8850

269

\(2 x^{2} y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0\)

8851

270

\(x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0\)

8852

271

\(2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\)

8853

272

\(2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0\)

8854

273

\(x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0\)

8855

274

\(4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0\)

8856

275

\(u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0\)

8857

276

\(u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0\)

8858

277

\(u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0\)

8859

278

\(u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0\)

8860

279

\(u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0\)

8861

280

\(y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}\)

8862

281

\(y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}\)

8863

282

\(x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y = 0\)

8864

283

\(x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0\)

8865

284

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y = 0\)

8866

285

\(y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}\)

8867

286

\(x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0\)

8868

287

\(\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0\)

8869

288

\(\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0\)

8870

289

\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

8871

290

\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

8872

291

\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\)

8873

292

\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\)

8874

293

\(\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

8875

294

\(y^{\prime \prime }-y^{\prime } x -3 y = 0\)

8876

295

\(\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

8877

296

\(y^{\prime \prime }-y^{\prime } x +2 y = 0\)

8878

297

\(\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0\)

8879

298

\(x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0\)

8880

299

\(2 x y^{\prime \prime }-y^{\prime }+2 y = 0\)

8881

300

\(x y^{\prime \prime }+y^{\prime } x -2 y = 0\)

8882

301

\(x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0\)

8883

302

\(y^{\prime \prime }-2 y^{\prime } x +y x^{2} = 0\)

8884

303

\(x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0\)

8885

304

\(x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right ) = 0\)

8886

305

\(2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0\)

8887

306

\(x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0\)

8888

307

\(x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0\)

8889

309

\(y^{\prime \prime }-2 y^{\prime } x +8 y = 0\)

8890

310

\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0\)

8891

311

\(x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0\)

8892

313

\(x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0\)

8893

314

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

8894

315

\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

8895

316

\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0\)

8896

317

\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0\)

8897

318

\(y^{\prime \prime }-y^{\prime } x +2 y = 0\)

8898

319

\(\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0\)

8899

320

\(\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0\)

8900

321

\(\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0\)

8901

322

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

8902

325

\(x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0\)

8903

326

\(2 x y^{\prime \prime }-y^{\prime }+2 y = 0\)

8904

327

\(2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0\)

8905

328

\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0\)

8906

329

\(x y^{\prime \prime }+2 y^{\prime }-x y = 0\)

8907

330

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

8908

331

\(x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0\)

8909

332

\(x^{4} y^{\prime \prime }+\lambda y = 0\)

8910

333

\(4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0\)

8911

334

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0\)

8912

335

\(x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0\)

8913

336

\(x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0\)

8914

337

\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

8915

338

\(16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y = 0\)

8916

339

\(y^{\prime \prime }-x^{2} y^{\prime }+x y = 0\)

8917

340

\(x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0\)

8918

341

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

8919

342

\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

8920

343

\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\)

8921

344

\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y = 0\)

8922

345

\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\)

8923

346

\(x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0\)

8924

347

\(2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0\)

8925

348

\(x y^{\prime \prime }+2 y^{\prime }+4 x y = 0\)

8926

349

\(x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0\)

8927

350

\(x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0\)

8928

351

\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\)

8929

352

\(x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0\)

8930

353

\(4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0\)

8931

354

\(2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (-3+2 t \right ) y^{\prime }-8 y = 0\)

8932

355

\(3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0\)

8933

356

\(x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0\)

8934

357

\(x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4} = 0\)

8935

358

\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\)

8936

359

\(x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0\)

8937

360

\(x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0\)

8938

361

\(x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0\)

8939

362

\(2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = 0\)

8940

363

\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\)

8941

364

\(y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0\)

8942

365

\(u^{\prime \prime }+\frac {u}{x^{2}} = 0\)

8943

366

\(u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0\)

8944

367

\(y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0\)

8945

368

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

8946

369

\(y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0\)

8947

370

\(y^{\prime \prime }+\frac {y}{2 x^{4}} = 0\)

8948

371

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8949

372

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8950

373

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8951

374

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8952

375

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8953

376

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8954

377

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8955

378

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8956

379

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8957

380

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8958

381

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

8959

382

\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\)

8960

383

\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x -x y = 0\)

8961

384

\(x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0\)

8962

385

\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\)

8963

388

\(x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0\)

8964

389

\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\)

8965

390

\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\)

8966

391

\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

8967

392

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

8968

394

\(x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y = 0\)

8969

395

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

8970

396

\(x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y = 0\)

8971

398

\(y^{\prime \prime } = \left (x^{2}+3\right ) y\)

8972

399

\(y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y = 0\)

8973

400

\(x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x} = 0\)

8974

401

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

8975

402

\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\)

8976

404

\(y^{\prime \prime }-y^{\prime }+y = 0\)

8977

405

\(\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

8978

406

\(x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\)

8979

407

\(\left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y = 0\)

8980

408

\(\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\)

8981

409

\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

8982

410

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

8983

411

\(\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0\)

8984

412

\(\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0\)

8985

413

\(\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0\)

8986

414

\(3 y^{\prime \prime }+y^{\prime } x -4 y = 0\)

8987

415

\(5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0\)

8988

416

\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\)

8989

417

\(\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\)

8990

418

\(y^{\prime \prime }+y^{\prime } x -2 y = 0\)

8991

419

\(\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0\)

8992

420

\(\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0\)

8993

421

\(t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0\)

8994

422

\(t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0\)

8995

423

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

8996

424

\(x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0\)

8997

425

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

8998

426

\(t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0\)

8999

427

\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\)

9000

428

\(\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0\)

9001

429

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

9002

430

\(t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0\)

9003

431

\(\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0\)

9004

432

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

9005

433

\(\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0\)

9006

434

\(\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\)

9007

435

\(2 y^{\prime \prime }+y^{\prime } x +3 y = 0\)

9008

436

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

9009

437

\(\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\)

9010

438

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

9011

439

\(\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0\)

9012

440

\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\)

9013

441

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

9014

442

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

9015

444

\(\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0\)

9016

445

\(\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0\)

9017

446

\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\)

9018

447

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\)

9019

448

\(x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = 0\)

9020

449

\(x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = 0\)

9021

450

\(\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = 0\)

9022

451

\(2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0\)

9023

452

\(x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0\)

9024

453

\(4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0\)

9025

454

\(x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0\)

9026

455

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

9027

456

\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\)

9028

457

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

9029

458

\(x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y = 0\)

9030

460

\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\)

9031

461

\(\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y = 0\)

9032

462

\(\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0\)

9033

463

\(x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y = 0\)

9034

464

\(\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0\)

9035

465

\(\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = 0\)

9036

466

\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\)

9037

467

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\)

9038

468

\(\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0\)

9039

469

\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0\)

9040

470

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

9041

472

\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0\)

9042

473

\(4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y = 0\)

9043

474

\(x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y = 0\)

9044

475

\(x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0\)

9045

476

\(x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0\)

9046

477

\(x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = 0\)

9047

478

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

9048

479

\(4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0\)

9049

480

\(\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0\)

9050

481

\(\left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y = 0\)

9051

482

\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (2-x \right ) y = 0\)

9052

483

\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0\)

9053

484

\(x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0\)

9054

485

\(x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0\)

9055

486

\(\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y = 0\)

9056

487

\(\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0\)

9057

488

\(\left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y = 0\)

9058

489

\(\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y = 0\)

9059

490

\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0\)

9060

491

\(\left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y = 0\)

9061

492

\(\left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y = 0\)

9062

493

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

9063

495

\(\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y = 0\)

9064

496

\(y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0\)

9065

497

\(\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0\)

9066

498

\(\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0\)

9067

499

\(\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0\)

9068

500

\(\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0\)

9069

501

\(y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0\)

9070

502

\(\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0\)

9071

503

\(y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0\)

9072

504

\(\left (3 x +1\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0\)

9073

505

\(\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0\)

9074

506

\(\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0\)

9075

507

\(\left (4+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0\)

9076

508

\(\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0\)

9077

509

\(x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0\)

9078

510

\(\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0\)

9079

511

\(\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0\)

9080

512

\(y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0\)

9081

513

\(\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0\)

9082

514

\(y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y = 0\)

9083

515

\(2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0\)

9084

516

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\)

9085

517

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\)

9086

518

\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\)

9087

519

\(3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0\)

9088

520

\(12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0\)

9089

521

\(y^{\prime \prime }+3 y^{\prime }+4 y = 0\)

9090

522

\(18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0\)

9091

523

\(2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0\)

9092

524

\(2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y = 0\)

9093

525

\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0\)

9094

526

\(2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y = 0\)

9095

527

\(3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\)

9096

528

\(2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0\)

9097

529

\(x^{2} \left (4+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\)

9098

530

\(2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0\)

9099

531

\(6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y = 0\)

9100

532

\(x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0\)

9101

533

\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0\)

9102

534

\(x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0\)

9103

535

\(8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\)

9104

536

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0\)

9105

537

\(x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0\)

9106

538

\(4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0\)

9107

539

\(3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0\)

9108

540

\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0\)

9109

541

\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0\)

9110

542

\(2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0\)

9111

543

\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0\)

9112

544

\(2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0\)

9113

545

\(9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0\)

9114

546

\(6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0\)

9115

547

\(9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\)

9116

548

\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0\)

9117

549

\(8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0\)

9118

550

\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0\)

9119

551

\(6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0\)

9120

552

\(28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0\)

9121

553

\(8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0\)

9122

554

\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0\)

9123

555

\(3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\)

9124

556

\(4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0\)

9125

557

\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\)

9126

558

\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\)

9127

559

\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0\)

9128

560

\(x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\)

9129

561

\(4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0\)

9130

562

\(x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0\)

9131

563

\(9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0\)

9132

564

\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0\)

9133

565

\(16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0\)

9134

566

\(9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0\)

9135

567

\(36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0\)

9136

568

\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0\)

9137

569

\(x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0\)

9138

570

\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0\)

9139

571

\(2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0\)

9140

572

\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0\)

9141

573

\(x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0\)

9142

574

\(x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0\)

9143

575

\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\)

9144

576

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0\)

9145

577

\(4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\)

9146

578

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0\)

9147

579

\(2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0\)

9148

580

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0\)

9149

581

\(4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0\)

9150

582

\(3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0\)

9151

583

\(9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0\)

9152

584

\(x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\)

9153

585

\(x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y = 0\)

9154

586

\(x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0\)

9155

587

\(x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0\)

9156

588

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0\)

9157

589

\(9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0\)

9158

590

\(x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0\)

9159

591

\(4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0\)

9160

592

\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0\)

9161

593

\(9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0\)

9162

594

\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0\)

9163

595

\(16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0\)

9164

596

\(x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0\)

9165

597

\(4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0\)

9166

598

\(x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0\)

9167

599

\(9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0\)

9168

600

\(2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0\)

9169

601

\(x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0\)

9170

602

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0\)

9171

603

\(x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 y x^{2} = 0\)

9172

604

\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0\)

9173

605

\(2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0\)

9174

606

\(x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y = 0\)

9175

607

\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0\)

9176

608

\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0\)

9177

609

\(x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0\)

9178

610

\(x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0\)

9179

611

\(4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0\)

9180

612

\(3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0\)

9181

613

\(x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0\)

9182

614

\(x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0\)

9183

615

\(x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0\)

9184

616

\(x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0\)

9185

617

\(4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0\)

9186

618

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0\)

9187

619

\(x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0\)

9188

620

\(x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0\)

9189

621

\(x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0\)

9190

622

\(x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0\)

9191

623

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 y x^{2} = 0\)

9192

624

\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0\)

9193

625

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0\)

9194

626

\(x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0\)

9195

627

\(4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0\)

9196

628

\(y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0\)

9197

629

\(y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0\)

9198

630

\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0\)

9199

631

\(\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0\)

9200

632

\(\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0\)

9201

633

\(\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0\)

9202

634

\(t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0\)

9203

635

\(y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0\)

9204

636

\(y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0\)

9205

638

\(2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0\)

9206

639

\(2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0\)

9207

640

\(2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0\)

9208

641

\(2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0\)

9209

642

\(t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0\)

9210

643

\(t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0\)

9211

644

\(t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0\)

9212

645

\(t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0\)

9213

646

\(t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0\)

9214

647

\(t y^{\prime \prime }+t y^{\prime }+2 y = 0\)

9215

648

\(t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0\)

9216

649

\(t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0\)

9217

650

\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0\)

9218

651

\(\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y = 0\)

9219

652

\(4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0\)

9220

653

\(f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0\)

9221

654

\(z y^{\prime \prime }-2 y^{\prime }+y z = 0\)

9222

655

\(z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0\)

9223

656

\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\)

9224

657

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

9225

658

\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

9226

659

\(4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y = 0\)

9227

660

\(x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 0\)

9228

661

\(y^{\prime \prime }+2 y^{\prime } x +4 y = 0\)

9229

662

\(y^{\prime \prime }+y^{\prime } x +3 y = 0\)

9230

663

\(y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0\)

9231

664

\(\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y = 0\)

9232

665

\(\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0\)

9233

666

\(y^{\prime \prime }+y^{\prime } x +\left (x +2\right ) y = 0\)

9234

667

\(\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0\)

9235

668

\(4 y^{\prime \prime }+y^{\prime } x +4 y = 0\)

9236

669

\(y^{\prime \prime }+y^{\prime } x -4 y = 0\)

9237

670

\(4 x y^{\prime \prime }-y^{\prime } x +2 y = 0\)

9238

671

\(6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0\)

9239

672

\(3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y = 0\)

9240

673

\(2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0\)

9241

674

\(4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0\)

9242

675

\(x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0\)

9243

676

\(x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0\)

9244

677

\(x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0\)

9245

678

\(x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0\)

9246

679

\(x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0\)

9247

680

\(x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0\)

9248

681

\(x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0\)

9249

682

\(x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0\)

9250

683

\(x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0\)

9251

684

\(x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0\)

9252

685

\(x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0\)

9253

686

\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0\)

9254

687

\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (2+3 x \right ) y = 0\)

9255

688

\(x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0\)

9256

689

\(4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0\)

9257

690

\(x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0\)

9258

691

\(x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0\)

9259

692

\(4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0\)

9260

693

\(x^{2} y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (x +2\right ) y = 0\)

9261

694

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0\)

9262

695

\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\)

9263

696

\(2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0\)

9264

697

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

9265

698

\(x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0\)

9266

699

\(x^{4} y^{\prime \prime }+y^{\prime } x +y = 0\)

9267

700

\(x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0\)

9268

701

\(\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0\)

9269

702

\(x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0\)

9270

703

\(x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y = 0\)

9271

704

\(x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 x y}{16} = 0\)

9272

705

\(x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0\)

9273

706

\(x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0\)

9274

707

\(x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0\)

9275

708

\(2 x^{2} y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0\)

9276

709

\(x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0\)

9277

710

\(2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0\)

9278

711

\(2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0\)

9279

712

\(x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0\)

9280

713

\(4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0\)

9281

714

\(u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0\)

9282

715

\(u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0\)

9283

716

\(u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0\)

9284

717

\(u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0\)

9285

718

\(u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0\)

9286

719

\(y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}\)

9287

720

\(y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}\)

9288

721

\(x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y = 0\)

9289

722

\(x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0\)

9290

723

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y = 0\)

9291

724

\(y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}\)

9292

725

\(x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0\)

9293

726

\(\left (2-x \right ) x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0\)

9294

727

\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

9295

728

\(x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 0\)

9296

729

\(3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0\)

9297

730

\(x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0\)

9298

731

\(\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0\)

9299

732

\(\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0\)

9300

733

\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

9301

734

\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

9302

735

\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\)

9303

736

\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\)

9304

737

\(\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

9305

738

\(y^{\prime \prime }-y^{\prime } x -3 y = 0\)

9306

739

\(\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

9307

740

\(y^{\prime \prime }-y^{\prime } x +2 y = 0\)

9308

741

\(\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0\)

9309

742

\(x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0\)

9310

743

\(2 x y^{\prime \prime }-y^{\prime }+2 y = 0\)

9311

744

\(x y^{\prime \prime }+y^{\prime } x -2 y = 0\)

9312

745

\(x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0\)

9313

746

\(y^{\prime \prime }-2 y^{\prime } x +y x^{2} = 0\)

9314

747

\(x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0\)

9315

748

\(x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right ) = 0\)

9316

749

\(2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0\)

9317

750

\(x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0\)

9318

751

\(x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0\)

9319

754

\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0\)

9320

755

\(x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0\)

9321

757

\(x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0\)

9322

758

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

9323

759

\(\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

9324

760

\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0\)

9325

761

\(\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0\)

9326

762

\(y^{\prime \prime }-y^{\prime } x +2 y = 0\)

9327

763

\(\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0\)

9328

764

\(\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0\)

9329

765

\(\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0\)

9330

766

\(\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0\)

9331

769

\(x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0\)

9332

770

\(2 x y^{\prime \prime }-y^{\prime }+2 y = 0\)

9333

771

\(2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0\)

9334

772

\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0\)

9335

773

\(x y^{\prime \prime }+2 y^{\prime }-x y = 0\)

9336

774

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

9337

775

\(x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0\)

9338

776

\(x^{4} y^{\prime \prime }+\lambda y = 0\)

9339

777

\(4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0\)

9340

778

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0\)

9341

779

\(x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0\)

9342

780

\(x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0\)

9343

781

\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

9344

782

\(16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y = 0\)

9345

783

\(y^{\prime \prime }-x^{2} y^{\prime }+x y = 0\)

9346

784

\(x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0\)

9347

785

\(y^{\prime \prime }+y^{\prime } x +2 y = 0\)

9348

786

\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0\)

9349

787

\(y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0\)

9350

788

\(\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y = 0\)

9351

789

\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\)

9352

790

\(x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0\)

9353

791

\(2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0\)

9354

792

\(x y^{\prime \prime }+2 y^{\prime }+4 x y = 0\)

9355

793

\(x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0\)

9356

794

\(x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0\)

9357

795

\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\)

9358

796

\(x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0\)

9359

797

\(4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0\)

9360

798

\(2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (-3+2 t \right ) y^{\prime }-8 y = 0\)

9361

799

\(3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0\)

9362

800

\(x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0\)

9363

801

\(x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4} = 0\)

9364

802

\(x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0\)

9365

803

\(x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0\)

9366

804

\(x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0\)

9367

805

\(x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0\)

9368

806

\(2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = 0\)

9369

807

\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\)

9370

808

\(y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0\)

9371

809

\(u^{\prime \prime }+2 u^{\prime }+u = 0\)

9372

810

\(u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0\)

9373

811

\(y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0\)

9374

812

\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

9375

813

\(y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0\)

9376

815

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9377

816

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9378

817

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9379

818

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9380

819

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9381

820

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9382

821

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9383

822

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9384

823

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9385

824

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9386

825

\(y^{\prime \prime }-y^{\prime } x -x y = 0\)

9387

826

\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\)

9388

827

\(2 x^{2} y^{\prime \prime }+3 y^{\prime } x -x y = 0\)

9389

828

\(x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0\)

9390

829

\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\)

9391

830

\(x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0\)

9392

831

\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0\)

9393

832

\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\)

9394

833

\(x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0\)

9395

834

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

9396

835

\(x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y = 0\)

9397

836

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

9398

837

\(x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y = 0\)

9399

838

\(y^{\prime \prime } = \left (x^{2}+3\right ) y\)

9400

839

\(y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y = 0\)

9401

840

\(x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0\)

9402

841

\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0\)

9403

843

\(y^{\prime \prime } = 0\)

9404

844

\(y^{\prime \prime } = \frac {2 y}{x^{2}}\)

9405

845

\(y^{\prime \prime } = \frac {6 y}{x^{2}}\)