# GSEB Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.1

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.1

Determine orders and degrees (if defined) of the differential equations given ¡n questions 1 to 10:
Question 1.
$$\frac{d^{4} y}{d x^{4}}$$ + sin(y”’) = 0
Solution:
∴ Order : 4
∴ Degree : It is not a polynomial in derivatives. Question 2.
y’ + 5y = 0
Solution:
∴ Order : 1
∴ Degree : 1

Question 3.
($$\frac{ds}{dt}$$)4 + 3($$\frac{d^{2} s}{d t^{2}}$$) = 0
Solution:
∴ Order : 2
∴ Degree : 1

Question 4.
($$\frac{d^{2} y}{d x^{2}}$$)2 + cos ($$\frac{dy}{dx}$$) = 0
Solution:
∴ Order : 2
∴ Degree : Not a polynomial in derivatives. Question 5.
($$\frac{d^{2} y}{d x^{2}}$$) = cos 3x + sin 3x
Solution:
∴ Order : 2
∴ Degree : 1

Question 6.
(y”’)2 + (y”)3 + (y’)4 + y5 = 0
Solution:
∴ order : 3
∴ Degree : 2

Question 7.
y”’ + 2y” + y’ = 0
Solution:
∴ Order : 3
∴ Degree : 1 Question 8.
y’ + y = ex
Solution:
∴ Order : 1
∴ Degree : 1

Question 9.
y” + (y’)2 + 2y = 0
Solution:
∴ Order : 2
∴ Degree : 1

Question 10.
y” + 2y’ + sin y = 0
Solution:
∴ Order : 2
∴ Degree : 1 Choose the correct answers in the following questions 11 and 12:

Question 11.
The degree of differential equation
$$\left(\frac{d^{2} y}{d x^{2}}\right)$$3 + ($$\frac{1}{2}$$)2 + sin($$\frac{dy}{dx}$$) + 1 = 0 is
(A) 1
(B) 2
(C) 1
(D) not defined
Solution:
Part (D) is the correct answer, since equation contain sin ($$\frac{dy}{dx}$$), which does not form a polynomial in derivatives. Question 12.
The order of differential equation 2x2$$\frac{d^{2} y}{d x^{2}}$$ – 3$$\frac{dy}{dx}$$ + y = 0 is
(A) 1
(B) 1
(C) 0
(D) not defined
Solution:
Order of given differential equation is 2.
∴ Part (A) is the correct answer.