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 = 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 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.