NCERT Solutions
Class 12 - Mathematics Part-2 - Chapter 9: DIFFERENTIAL EQUATIONS
Exercise 9.1

Question. 1

Determine order and degree (if defined) of the differential equation \(\frac{d^4y}{dx^4} + \sin(y''') = 0\).

Answer:

Order 4; Degree not defined

Question. 2

Determine order and degree (if defined) of the differential equation \(y' + 5y = 0\).

Answer:

Order 1; Degree 1

Question. 3

Determine order and degree (if defined) of the differential equation \(\left(\frac{ds}{dt}\right)^4 + 3s\frac{d^2s}{dt^2} = 0\).

Answer:

Order 2; Degree 1

Question. 4

Determine order and degree (if defined) of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2 + \cos\left(\frac{dy}{dx}\right) = 0\).

Answer:

Order 2; Degree not defined

Question. 5

Determine order and degree (if defined) of the differential equation \(\frac{d^2y}{dx^2} = \cos 3x + \sin 3x\).

Answer:

Order 2; Degree 1

Question. 6

Determine order and degree (if defined) of the differential equation \((y''')^2 + (y'')^3 + (y')^4 + y^5 = 0\).

Answer:

Order 3; Degree 2

Question. 7

Determine order and degree (if defined) of the differential equation \(y''' + 2y'' + y' = 0\).

Answer:

Order 3; Degree 1

Question. 8

Determine order and degree (if defined) of the differential equation \(y' + y = e^x\).

Answer:

Order 1; Degree 1

Question. 9

Determine order and degree (if defined) of the differential equation \(y'' + (y')^2 + 2y = 0\).

Answer:

Order 2; Degree 1

Question. 10

Determine order and degree (if defined) of the differential equation \(y'' + 2y' + \sin y = 0\).

Answer:

Order 2; Degree 1

Question.  11

The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^2 + \sin\left(\frac{dy}{dx}\right) + 1 = 0\) is

(A)

3

(B)

2

(C)

1

(D)

not defined

Question.  12

The order of the differential equation \(2x^2\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + y = 0\) is

(A)

2

(B)

1

(C)

0

(D)

not defined

NCERT Solutions Class 12 – Mathematics Part-2 – Chapter 9: DIFFERENTIAL EQUATIONS – Exercise 9.1 | Detailed Answers