Download OU B-Tech First Year 2015 June 9356 Faculty Of Engineering Question Paper

Download OU (Osmania University) B.Tech (Bachelor of Technology) First Year (1st Year) 2015 June 9356 Faculty Of Engineering Question Paper

Code No. 9356 / N
FACULTY OF ENGINEERING
B.E. I ? Year (New) (Main) Examination, May / June 2015
Subject : Mathematics - II
Time : 3 Hours
Max. Marks: 75
Note: Answer all questions from Part - A and answer any five questions from Part -B.
PART ? A (25 Marks)
1 Find the values of a and b such that (3ax
2
+ 2eY)dx + (2bxeY+3y)dy=0 is exact. (2)
2 Obtain the general solution of the Clairaut's equation y = xy' + (y')
3
.
(3)
3 If yi=e
2x
is a solution of y" ? 5y' + 6y = 0, find the second linearly independent
solution.
(2)
4 Find a particular integral of (D2-1)y=x4.
(3)
5 Does the differential equation x
3
y"+xy'+y=0 have a Frobenius-series.solution about
x = 0? Give a reason.
(2)
6 Using Rodrigue's formula, find P2(x).
(3)
7 Define error function. Prove that erf(-x) = -erf(x).
(2)
8 Evaluate x
4
J
3
(x)dx in terms of Besse' functions.
(3)
(2)
10 Find the inverse Laplace transform
PART ? B (50 Marks)
11 (a) Solve (x
3
- 2y
2
)dx + 2xy
(b) If the temperature of air
g
:is: 0
?
C,:pnd a body cools from 140
?
C to 80
?
C in
20 minutes, find when the te 'm 'perature will be 35
?
C.
12 (a) Solve y" y' 6y =
(b) Find the solution of
dy
the system of equations
1
= y, + y
day',
2
, - =9y, + y,
di di
13
Find the poweseries solution of the differential equation (1 + x)y" + y' + 3y =0
about x 0.
14 (a) EVNU4te sin B cos' 0 dO using Beta and Gamma functions.
0

(b) Prove that 1,,
2
(x)= sin x
Trx
15 (a) Find L{e
-2t
(2 sint ? 4 cosh t)}.
(b) Solve y" + 2y' ? 3y =0, y(0)=0, y'(0)=4 using Laplace transforms.
16 (a) Find the orthogonal trajectories of the family of curves r
ri
cosn 0=a
n
, a is the
parameter,
(b) Solve x
3
y"' + 4x
2
y" + 2xy' ? 2y = 0.
17 (a) Prove that f (x)dx
2/7
2
+1
(b) Find L
-1

1 }
using convolution theorem,
9 Find L

(
3
)
(5)
(
5
)
(
5
)
(
5
)
(10)
(
5
)
(5)
(
5
)
(
5
)
(
5
)
(5)
(
5
)
(5)
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