Class 12 NCERT Solutions- Mathematics Part II – Chapter 9 Differential Equations-Exercise -9.1

Determine order and degree (if defined) of differential equations given in exercises 1 to 10.

Question 1. 

Solution:

Given: 

Here the order is 4 and degree is not defined because it is not a polynomial function.

Question 2. y’ + 5y = 0

Solution:

Given: y’ + 5y = 0

Here, the order is 1 and the degree is also 1.

Question 3. 

Solution:

Given: 

Here, the order is 2 and the degree is 1.

Question 4. 

Solution:

Given: 

Here, the order is 2 and degree is not defined because it is not a polynomial function.

Question 5. 

Solution:

Given: 

Here, the order is 2 and degree is 1.

Question 6. (y”’)² + (y”)³ + y(‘)⁴ + y⁵ = 0

Solution:

Given: (y”’)² + (y”)³ + y(‘)⁴ + y⁵ = 0

The order is 3 and the degree is 2.

Question 7. y” + 2y” + y’ = 0

Solution:

Given: y”’ + 2y” + y’ = 0

The order is 3 and the degree is 1

Question 8. y’ + y = e^x

Solution:

Given: y’ + y = e^x

The order is 1 and the degree is 1.

Question 9. y” + (y’)² + 2y = 0

Solution:

Given: y” + (y’)² + 2y = 0

The order is 3 the degree is 1

Question 10. y” + 2y’ + sin y = 0

Solution:

Given: y” + 2y’ + sin y = 0

The order is 2 and the degree is one.

Question 11. The degree of the differential equation

is 

(A) 3          (B) 2          (C) 1          (D) Not defined

Solution:

Given: 

Here, the degree is not defined.     

So, the correct option is D.

Question 12. The order of the differential equation

is

(A) 3          (B) 2          (C) 1           (D) Not defined

Solution:

Given: 

Here, the order is 2. 

So, the correct option is A.

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