NCERT Class 12-Mathematics: Chapter –9 Differential Equations Part 3

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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.