NCERT Class 12-Mathematics: Chapter – 9 Differential Equations Part 17 (For CBSE, ICSE, IAS, NET, NRA 2022)
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Question 76: Fill in the blanks of the following (i to xi)
(i) The degree of the differential equation is ________.
Answer: Not defined
(ii) The degree of the differential equation is ________.
Answer: Not defined
(iii) The number of arbitrary constants in the general solution of a differential equation of order three is ________.
Answer: (3)
(iv) is an equation of the type ________.
Answer:
(v) General solution of the differential equation of the type is given by ________.
Answer:
(vi) The solution of the differential equation is________.
Answer:
(vii) The solution of is________.
Answer:
(viii) The solution of the differential equation is ________.
Answer:
(ix) General solution of is ________.
Answer:
(x) The solution of differential equation is ________.
Answer:
(xi) The integrating factor of is ________.
Answer:
Question 77: State True or False for the following:
(i) Integrating factor of the differential of the form is given by
Answer: True
(ii) Solution of the differential equation of the type is given by
Answer: True
(iii) Correct substitution for the solution of the differential equation of the type ) , where ) is a homogeneous function of zero degree is .
Answer: True
(iv) Correct substitution for the solution of the differential equation of the type where is a homogeneous function of the degree zero is .
Answer: True
(v) Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Answer: False
(vi) The differential equation representing the family of circles will be of order two.
Answer: False
(vii) The solution of
Answer: True
(viii) Differential equation representing the family of curves is
Answer: True
(ix) The solution of the differential equation .
Answer: True
(x) Solution of
Answer: True
(xi) The differential equation of all non-horizontal lines in a plane is
Answer: True