Subject Code : KAS-203 Subject : Engg Mathematics II B ...
Transcript of Subject Code : KAS-203 Subject : Engg Mathematics II B ...
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