# Class 12 Maths NCERT Solutions for Chapter 9 Differential Equations Exercise 9.1

### Differential Equations Exercise 9.1 Solutions

**1. Determine order and degree (If defined) of differential equation d ^{4}y /dx^{4} + sin(y') = 0 **

**Solution**

d^{4}y /dx^{4} + sin(y''') = 0

⇒ y''' + sin(y''') = 0

The highest order derivative present in the differential equation is y''''. Therefore, its order is four.

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.

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

**Solution**

The given differential equation is :

y' + 5y = 0

The highest order derivative present in the differential equation is y' . Therefore, its order is one.

It is a polynomial equation in y'. The highest power raised to y' is 1. Hence, its degree is one.

**3. Determine order and degree (if defined of differential equation (ds/dt) ^{4} + 3s d^{2}s/dt^{2} = 0 **

**Solution**

The highest order derivative present in the given differential equation is d

^{2}s/dt

^{2}. Therefore, its order is two .

^{2}s/dt

^{2}and ds/dt. The power raised to d

^{2}s/dt

^{2}is 1.

**4. Determine order and degree (if defined) of differential equation d**

^{2}y/(ds^{2})^{2}+ cos (dy/dx) = 0**Solution**

The highest order derivative present in the given differential equation is d

^{2}y/dx

^{2}. Therefore, its order is 2.

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.

**5. Determine order and degree (if defined) of differential equation d**

^{2}y/dx^{2}= cos 3x + sin 3x**Solution**

^{2}y/dx

^{2}= cos 3x + sin 3x

⇒ d

^{2}y/dx

^{2}- cos 3x - sin 3x = 0

The highest order derivative present in the differential equation is d

^{2}y/dx

^{2}. Therefore, its order is two.

^{2}y/dx

^{2}and the power raised to d

^{2}y/dx

^{2}is 1.

**6. Determine order and degree (if defined) of differential equation**

**(y''') + (y'')**

^{3}+ (y')^{4}+ y^{5}= 0**Solution**

^{3}+ (y')

^{4}+ y

^{5}= 0

The highest order derivative present in the differential equation is y'''. Therefore, its order is three.

The highest power raised to y''' is 2. Hence, its degree is 2.

**7. Determine order and degree(if defined) of differential equation y′′′ + 2y″ + y′ = 0**

**Solution**

The highest order derivative present in the differential equation is y'''. Therefore, its order is three.

**8. Determine order and degree(if defined) of differential equation y′ + y = e**

^{x}.**Solution**

^{x}

⇒ y' + y - e

^{x}= 0

The highest order derivative present in the differential equation is y'. Therefore, its order is one.

The given differential equation is a polynomial equation in y' and the highest power raised to y' is one. Hence, its degree is one.

**9. Determine order and degree (if defined) of differential equation y'' + (y')**

^{2}+ 2y = 0**Solution**

^{2}+ 2y = 0

The highest order derivative present in the differential equation is y''. Therefore, its order is two.

**10. Determine order and degree(if defined) of differential equation y″ + 2y′ + sin y = 0**

**Solution**

The highest order derivative present in the differential equation is y''. Therefore, its order is two.

Hence, its degree is one.

**11. The degree of the differential equation**

(d

(d

^{2}y/dx^{2})^{3}+ (dy/dx)^{2}+ sin(dy/dx) + 1 = 0**(A) 3**

(B) 2

(C) 1

(D) not defined

(B) 2

(C) 1

(D) not defined

**Solution**

The given differential equation is not a polynomial equation in its derivatives. Therefore, its degree is not defined.

**12. The order of the differential equation 2x**

^{2}(d^{2}y/dx^{2}) + 3(dy/dx) + y = 0 is**(A) 2**

(B) 1

(C) 0

(D) not defined

(B) 1

(C) 0

(D) not defined

**Solution**

The highest order derivative present in the given differential equation is d

^{2}y/dx

^{2}. Therefore, its order is two.