Download OU B-Tech First Year 2014 June 6003 Mathematics II Question Paper

Download OU (Osmania University) B.Tech (Bachelor of Technology) First Year (1st Year) 2014 June 6003 Mathematics II Question Paper

Code No. 6003 / M
FACULTY OF ENGINEERING and INFORMATICS
B.E. I Year (Main) Examination, June 2014
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 arbitrary constants a, b from
y = ae
3x
+ be
5x
,
2 Solve = + x
2

(IX
3 Solve y" y = 0,, when y = 0 and y = 2 at x = 0.
4 Find the particular integral of (D
2
+ 1)y = 8e
-x
.
5 Classify the singular points of (I + 2y = 0.
6 prove that P
n
(l) = 1.
7 Show that J,
;2
(x)
8 Prove that j" (ix = , ,C' ?1.
0 CI'
(C' +1)
(log (:)(
9 Find the Laplace transform of e
-t
cost.
+ 2
10 Find inverse Laplace transform of
.s.(s ? 3)(s + 2)
PART ? B (50 Marks)
11 a) Find the orthogonal trajectories of r = ce
9
, where C is the parameter.
b) Solve
d y
v = y
2
(sinx + cos x).
dx
12 a) Using the method of variation of parameters solve (D
2
+1) y = x .
b) Solve (0
2
? 4D + 2) y = 12e
x
sin2x.
13 Obtain the series solution of the equation
x
2
y
r,
Ay
r ?
(x
2
14 a) Prove that 130
.
71,
?
Fon +
b) Prove that fl
o
(x) .1
1
(x) dv
1

4)y=0 about x = 0,
2
------ cos x.
27X
(2)
(3)
(2)
(3)
(2)
(3)
(2)
(3)
(2)
(3)
(
5
)
(5)
(
5
)
(
5
)
(10)
(
5
)
(
5
)
....... . 2
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Code No. 6003 / M
FACULTY OF ENGINEERING and INFORMATICS
B.E. I Year (Main) Examination, June 2014
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 arbitrary constants a, b from
y = ae
3x
+ be
5x
,
2 Solve = + x
2

(IX
3 Solve y" y = 0,, when y = 0 and y = 2 at x = 0.
4 Find the particular integral of (D
2
+ 1)y = 8e
-x
.
5 Classify the singular points of (I + 2y = 0.
6 prove that P
n
(l) = 1.
7 Show that J,
;2
(x)
8 Prove that j" (ix = , ,C' ?1.
0 CI'
(C' +1)
(log (:)(
9 Find the Laplace transform of e
-t
cost.
+ 2
10 Find inverse Laplace transform of
.s.(s ? 3)(s + 2)
PART ? B (50 Marks)
11 a) Find the orthogonal trajectories of r = ce
9
, where C is the parameter.
b) Solve
d y
v = y
2
(sinx + cos x).
dx
12 a) Using the method of variation of parameters solve (D
2
+1) y = x .
b) Solve (0
2
? 4D + 2) y = 12e
x
sin2x.
13 Obtain the series solution of the equation
x
2
y
r,
Ay
r ?
(x
2
14 a) Prove that 130
.
71,
?
Fon +
b) Prove that fl
o
(x) .1
1
(x) dv
1

4)y=0 about x = 0,
2
------ cos x.
27X
(2)
(3)
(2)
(3)
(2)
(3)
(2)
(3)
(2)
(3)
(
5
)
(5)
(
5
)
(
5
)
(10)
(
5
)
(
5
)
....... . 2
Code No. 6003 / M
-2?
15 a) Apply convolution theorem to evaluate
(
5
)
(s
--
-2 +1)(s2+
b) Use Laplace transform to solve y' y = ex given that y(0) = 1.
(
5
)
16 a) Find the general solution and singular solution of the Clairaut's equation
(
5
)
y= (x ? a) p p
2
.
b) Solve the initial value problem ?2y' = 0 with y(0) = 1, ))
1
(0) = 0.
(
5
)
17 a) Prove that fi),?(x)1)?(x)cly = 0 if m 11 .
(
5
)
b) Find the Laplace transform of t sin
2
(3t).
(5)
* * *
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