3.9.1 Problems 1 to 100

Table 3.507: First order ode linear in derivative

#

ODE

Mathematica

Maple

1

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

2

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

3

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

4

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

5

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

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

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

11

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

12

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

13

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

14

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

15

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

16

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

17

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

18

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

19

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

20

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

21

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

22

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

23

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

24

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

25

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

26

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

27

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

28

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

29

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

30

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

31

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

32

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

33

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

34

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

35

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

36

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

37

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

38

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

39

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

40

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

41

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

42

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

43

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

44

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

45

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

46

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

47

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

48

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

49

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

50

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

51

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

52

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

53

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

54

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

55

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

56

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

57

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

58

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

59

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

60

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

61

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

62

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

63

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

64

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

65

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

66

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

67

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

68

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

69

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

70

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

71

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

72

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

73

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

74

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

75

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

76

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

77

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

78

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

79

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

80

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

81

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

82

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

83

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

84

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

85

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

86

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

87

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

88

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

89

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

90

\[ {}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}} \]

91

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

92

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

93

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

94

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

95

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

96

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

97

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

98

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

99

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

100

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