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} + y^{5} = 0

Solution:

∴ order : 3

∴ Degree : 2

Question 7.

y”’ + 2y” + y’ = 0

Solution:

∴ Order : 3

∴ Degree : 1

Question 8.

y’ + y = e^{x}

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 2x^{2}\(\frac{d^{2} y}{d x^{2}}\) – 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.