NCERT Class 12-Mathematics: Chapter – 9 Differential Equations Part 17 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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