5.9.1 Problems 1 to 100

Table 5.629: First order ode linear in derivative

#

ODE

Mathematica

Maple

1

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

2

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

3

\[ {}y^{\prime } = \sqrt {x} \]

4

\[ {}y^{\prime } = \frac {1}{x^{2}} \]

5

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

6

\[ {}y^{\prime } = x \sqrt {x^{2}+9} \]

7

\[ {}y^{\prime } = \frac {10}{x^{2}+1} \]

8

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

9

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

10

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

19

\[ {}y^{\prime } = -y-\sin \left (x \right ) \]

20

\[ {}y^{\prime } = x +y \]

21

\[ {}y^{\prime } = y-\sin \left (x \right ) \]

22

\[ {}y^{\prime } = x -y \]

23

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

24

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

25

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

26

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

27

\[ {}y^{\prime } = 2 x^{2} y^{2} \]

28

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

29

\[ {}y^{\prime } = y^{{1}/{3}} \]

30

\[ {}y^{\prime } = y^{{1}/{3}} \]

31

\[ {}y^{\prime } = \sqrt {x -y} \]

32

\[ {}y^{\prime } = \sqrt {x -y} \]

33

\[ {}y y^{\prime } = x -1 \]

34

\[ {}y y^{\prime } = x -1 \]

35

\[ {}y^{\prime } = \ln \left (1+y^{2}\right ) \]

36

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

37

\[ {}y^{\prime } = x +y \]

38

\[ {}y^{\prime } = y-x \]

39

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

40

\[ {}y^{\prime } = x +\frac {y^{2}}{2} \]

41

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

42

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

43

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

44

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

45

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

46

\[ {}y^{\prime } = 3 \sqrt {x y} \]

47

\[ {}y^{\prime } = 64^{{1}/{3}} \left (x y\right )^{{1}/{3}} \]

48

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

49

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

50

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

51

\[ {}y^{\prime } = x y^{3} \]

52

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

53

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

54

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

55

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

56

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

57

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

58

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

59

\[ {}y^{\prime } = y \,{\mathrm e}^{x} \]

60

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

61

\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]

62

\[ {}y^{\prime } = 4 x^{3} y-y \]

63

\[ {}1+y^{\prime } = 2 y \]

64

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

65

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

66

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

67

\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \]

68

\[ {}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2} \]

69

\[ {}y^{\prime } = y^{2} \]

71

\[ {}y^{\prime } = 2 \sqrt {y} \]

72

\[ {}y^{\prime } = y \sqrt {y^{2}-1} \]

73

\[ {}y^{\prime }+y = 2 \]

74

\[ {}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x} \]

75

\[ {}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x} \]

76

\[ {}y^{\prime }-2 x y = {\mathrm e}^{x^{2}} \]

77

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

78

\[ {}x y^{\prime }+5 y = 7 x^{2} \]

79

\[ {}2 x y^{\prime }+y = 10 \sqrt {x} \]

80

\[ {}3 x y^{\prime }+y = 12 x \]

81

\[ {}x y^{\prime }-y = x \]

82

\[ {}2 x y^{\prime }-3 y = 9 x^{3} \]

83

\[ {}x y^{\prime }+y = 3 x y \]

84

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

85

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

86

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

87

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

88

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

89

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

90

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

91

\[ {}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right ) \]

92

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

93

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

94

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

95

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

96

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

97

\[ {}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \]

101

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

102

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

103

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

104

\[ {}y^{\prime }+p \left (x \right ) y = q \left (x \right ) \]

105

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

106

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

107

\[ {}x y^{\prime } = y+2 \sqrt {x y} \]

108

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

109

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

110

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

111

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

112

\[ {}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}} \]