Download OU B-Tech First Year 2015 June 9003 Faculties Of Engineering and Informatics Question Paper

Download OU (Osmania University) B.Tech (Bachelor of Technology) First Year (1st Year) 2015 June 9003 Faculties Of Engineering and Informatics Question Paper

PART - B (50 Marks)
dy
11 a) Solve. cos x ? --- + y = tan x
Code No. 9003 / 0
FACULTIES OF ENGINEERING & INFORMATICS
B.E. I - Year (Old) Examination, May/ June 2015
Subject : Mathematics - II
Time : 3 hours Max. Marks : 75
Note: Answer all questions from Part-A. Answer any FIVE questions from Part-B.
PART A (25 Marks)
1 Form the differential equation by eliminating the arbitrary cons ppt 'c' from the
family of curves y = c(x c)
2
. 2
2 Solve y x ?
dy
= 3
(
1 - x
2
----
dy
3
dx dx
3 Solve
(
D 4
+8D
2
+ I 6)y = 0 , where D . 2
dx
4 Find the particular integral of (0
4
- aly = x
4
. 3
5 Find the Laplace transform of f(t) = cos(at+b)
,
whereb, b are any two constants. 2
6 Find the inverse Laplace transform of 3
F(S) =
S + 6
,
S' +65+13
7 Classify the singular points of the differentialequation 2
x
3
y" + 3x y'+ 6y = 0
8 Express f(x)=3P3(x)+2P2(x)1741(X)t5P
0
(x) as a polynomial in x, where P
m
(x) is
the legendre polynomial of'pr
-
Orin: 3
9 Evaluate f(x - a)"
-
' x interms of beta function, where m,n,a,b are
a
positive constants. 2
10 Evaluate
d.,
krt
.
*AA. 3
5
b) Obtain the general solution and singular solution of the following Clairaut's
equation.
5
Y x y
2
12 a) Find the general solution of the differential equation
5
y" + 4 / + 4y = 6 e
-2x
cos
b) Find the general solution of the differential equation y" + 4y = sec 2x, by the
method of variation of parameters.
5
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PART - B (50 Marks)
dy
11 a) Solve. cos x ? --- + y = tan x
Code No. 9003 / 0
FACULTIES OF ENGINEERING & INFORMATICS
B.E. I - Year (Old) Examination, May/ June 2015
Subject : Mathematics - II
Time : 3 hours Max. Marks : 75
Note: Answer all questions from Part-A. Answer any FIVE questions from Part-B.
PART A (25 Marks)
1 Form the differential equation by eliminating the arbitrary cons ppt 'c' from the
family of curves y = c(x c)
2
. 2
2 Solve y x ?
dy
= 3
(
1 - x
2
----
dy
3
dx dx
3 Solve
(
D 4
+8D
2
+ I 6)y = 0 , where D . 2
dx
4 Find the particular integral of (0
4
- aly = x
4
. 3
5 Find the Laplace transform of f(t) = cos(at+b)
,
whereb, b are any two constants. 2
6 Find the inverse Laplace transform of 3
F(S) =
S + 6
,
S' +65+13
7 Classify the singular points of the differentialequation 2
x
3
y" + 3x y'+ 6y = 0
8 Express f(x)=3P3(x)+2P2(x)1741(X)t5P
0
(x) as a polynomial in x, where P
m
(x) is
the legendre polynomial of'pr
-
Orin: 3
9 Evaluate f(x - a)"
-
' x interms of beta function, where m,n,a,b are
a
positive constants. 2
10 Evaluate
d.,
krt
.
*AA. 3
5
b) Obtain the general solution and singular solution of the following Clairaut's
equation.
5
Y x y
2
12 a) Find the general solution of the differential equation
5
y" + 4 / + 4y = 6 e
-2x
cos
b) Find the general solution of the differential equation y" + 4y = sec 2x, by the
method of variation of parameters.
5
Code No. 9003 / C.;
2
13 a) Solve the initial value problem 5
y" -4-
+ 5 y 8(t ? 3), y(0) = 0, y'(0) = 0 .
b) Find the inverse Laplace transform of F(S) = by using convolution
( z ?
theorem.
14 Obtain the series solution of the equation
x y" + xy = 0 about x = 0 by the Frobenius method.
5
10
15 a) Evaluate the improper integrals using Gamma function 5
i) E
x2
dx
ii) f (7
x3
d.)C
0.
b) State and prove the orthogonality of Chebyskev polynomials TO). 5
16 a) if the population of a country doubles in 0 years, in how many years will it
treble under the assumption that thdlate of increase is proportional to the
number of inhabitants. 5
b) Solve
d2Y
2 ?
dY
+ y = 5
dx
2
de

17 a) Find the Laplace transform of the function 5
sin/ if <7
-
/
-

0 if < t < 2.7r
and the period of f(t) is 2n .
b) Show that (2n+1)x P
r
,(x) = (n+1) P
n
+1 (x) +nP
n
_1(x) where P
ii
(x) is the
Legendre polynomial of degree n. 5
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