Problems 1 to 100

Table 4.625: First order ode linear in derivative


#	ODE	Mathematica	Maple	Sympy

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

37	\[ {} y^{\prime } = x +y \]	✓	✓	✓

38	\[ {} y^{\prime } = y-x \]	✓	✓	✓

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

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

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	\[ {} y^{\prime }+1 = 2 y \]	✓	✓	✓

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

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

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

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

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

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

4.9.1 Problems 1 to 100