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

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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)

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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 ?

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dy
= 3
(
1 - x
2

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----
dy
3
dx dx
3 Solve

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(
D 4
+8D
2
+ I 6)y = 0 , where D . 2

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dx
4 Find the particular integral of (0
4
- aly = x
4

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. 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

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F(S) =
S + 6
,
S' +65+13
7 Classify the singular points of the differentialequation 2

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x
3
y" + 3x y'+ 6y = 0
8 Express f(x)=3P3(x)+2P2(x)1741(X)t5P
0

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(x) as a polynomial in x, where P
m
(x) is
the legendre polynomial of'pr
-

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Orin: 3
9 Evaluate f(x - a)"
-
' x interms of beta function, where m,n,a,b are
a

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positive constants. 2
10 Evaluate
d.,
krt
.

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*AA. 3
5
b) Obtain the general solution and singular solution of the following Clairaut's
equation.
5

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Y x y
2
12 a) Find the general solution of the differential equation
5
y" + 4 / + 4y = 6 e

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-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

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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.

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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

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2 Solve y x ?
dy
= 3
(
1 - x

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2
----
dy
3
dx dx

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3 Solve
(
D 4
+8D
2

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+ I 6)y = 0 , where D . 2
dx
4 Find the particular integral of (0
4
- aly = x

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4
. 3
5 Find the Laplace transform of f(t) = cos(at+b)
,
whereb, b are any two constants. 2

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6 Find the inverse Laplace transform of 3
F(S) =
S + 6
,
S' +65+13

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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

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0
(x) as a polynomial in x, where P
m
(x) is
the legendre polynomial of'pr

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-
Orin: 3
9 Evaluate f(x - a)"
-
' x interms of beta function, where m,n,a,b are

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a
positive constants. 2
10 Evaluate
d.,
krt

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.
*AA. 3
5
b) Obtain the general solution and singular solution of the following Clairaut's
equation.

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5
Y x y
2
12 a) Find the general solution of the differential equation
5

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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.

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5
Code No. 9003 / C.;
2
13 a) Solve the initial value problem 5
y" -4-

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+ 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

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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

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x2
dx
ii) f (7
x3
d.)C

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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

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b) Solve
d2Y
2 ?
dY
+ y = 5

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dx
2
de

17 a) Find the Laplace transform of the function 5

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sin/ if <7
-
/
-

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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

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n
+1 (x) +nP
n
_1(x) where P
ii

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(x) is the
Legendre polynomial of degree n. 5
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