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Class 12 NCERT Solutions- Mathematics Part II – Chapter 9 Differential Equations-Exercise -9.1
  • Last Updated : 05 Mar, 2021

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

Question 1. \frac{d^4y}{dx^4}+\sin(y''')=0

Solution:

Given: \frac{d^4y}{dx^4}+\sin(y''')=0

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. (\frac{ds}{dt})^{4}+3s\frac{d^{2}s}{dt^{2}}=0

Solution:

Given: (\frac{ds}{dt})^{4}+3s\frac{d^{2}s}{dt^{2}}=0

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

Question 4. (\frac{d^{2}y}{dx^{2}})=\cos(\frac{dy}{dx})=0

Solution:

Given: (\frac{d^{2}y}{dx^{2}})=\cos(\frac{dy}{dx})=0

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

Question 5. (\frac{d^{2}y}{dx^{2}})=\cos3x+\sin3x

Solution:



Given: (\frac{d^{2}y}{dx^{2}})=\cos3x+\sin3x

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 = ex

Solution:

Given: y’ + y = ex

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

(\frac{d^2y}{dx^2})^{3}+(\frac{dy}{dx})^{2}+sin(\frac{dy}{dx})+1=0 is 

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

Solution:

Given: (\frac{d^2y}{dx^2})^{3}+(\frac{dy}{dx})^{2}+sin(\frac{dy}{dx})+1=0

Here, the degree is not defined.     

So, the correct option is D.

Question 12. The order of the differential equation

2x^1\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0 is

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

Solution:

Given: 2x^1\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0

Here, the order is 2. 

So, the correct option is A.

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