NCERT Class 12-Mathematics: Chapter – 9 Differential Equations Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 10:

Solve

Answer:

Given equation can be written as

Dividing both sides by , we get

Integrating both sides, we get

Substituting we get

is the required solution.

Question 11:

State the type of the differential equation for the equation. and solve it.

Answer:

Given equation can be written as i.e..

Clearly RHS of is a homogeneous function of degree zero. Therefore, the given equation is a homogeneous differential equation. Substituting , we get from (1)

Integrating both sides of (2) , we get

Objective Type Questions

Choose the Correct Answer from the Given Four Options in Each of the Examples 12 to 21

Question 12:

The degree of the differential equation is

(A)

(B)

(C)

(D)

Answer:

The correct answer is (B) .

Question 13:

The degree of the differential equation is

(A)

(B)

(C)

(D) Not defined

Answer:

Correct answer is (D) . The given differential equation is not a polynomial equation in terms of its derivatives, so its degree is not defined.

Question 14:

The order and degree of the differential equation respectively, are

(A)

(B)

(C)

(D)

Answer:

Correct answer is (C) .

Question 15:

The order of the differential equation of all circles of given radius a is:

(A)

(B)

(C)

(D)

Answer:

Correct answer is (B) .

Let the equation of given family be . It has two arbitrary constants and . Therefore, the order of the given differential equation will be 2.