Subject Code : KAS-203 Subject : Engg Mathematics II B.Tech.-SECOND SEMESTER

SECTION – A

1. Attempt all questions in brief. (1*5 = 5) Q N QUESTION

a. Find Particular integral of − 4푦 = 푒 .

Ans 풙풆ퟐ풙

ퟒ

b. Find C. F. of the equation is 푥 푦 + 푥푦 + 푦 = 0. Ans: 풄ퟏ풄풐풔풍풐품풙 + 풄ퟐ풔풊풏풍풐품풙

c. Test the convergence of the integral ∫ 푑푥. Ans: Divergent

d. Find the value of −

Ans: ퟒퟑ√흅

e. Evaluate ∫ 푥 (1 − 푥) 푑푥 Ans: ퟏ ퟓퟎퟒ

SECTION - B

2. Attempt any TWO of the following. (2*5 = 10)

Q N QUESTION

a.

Obtain the general solution of the differential equation 푦 − 2푦 + 2푦 = 푥 + 푒 푐표푠푥

b.

Solve the following simultaneous equation − 3푥 − 4푦 = 0

+ 푥 + 푦 = 0

c. Show that 훽(푙,푚) = ⌈ ⌈⌈

Ans: As per book

d.

Evaluate improper integral ∫√

푑푥

SECTION - C 3. Attempt any ONE part of the following : (1*5 = 5) Q N

QUESTION

a.

Solve by method of variation of parameters − 푦 =

b. Using Frobenius method, obtain a series solution in powers of 푥 for differential equation 2푥(1 − 푥) + (1 − 푥) + 3푦 = 0

4. Attempt any ONE part of the following : (1*5 = 5)

Q N QUESTION

a. Evaluate ∫( )( )

푑푥

b.

Using Beta and Gamma functions, evaluate ∫

5. Attempt any ONE part of the following : (1*5 = 5) Q N

QUESTION

a. Solve the following differential equation − 4푥 + (4푥 − 1)푦 = −3푒 푠푖푛2푥

b.

Solve − 푐표푡푥 − 푦푠푖푛 푥 = 푐표푠푥 − 푐표푠 푥