Download OU B-Tech First Year 2011 June 3313 Mathematics II Question Paper

Download OU (Osmania University) B.Tech (Bachelor of Technology) First Year (1st Year) 2011 June 3313 Mathematics II Question Paper

Code No. : 3313/N
FACULTY 01? ENGINEERING & INFORMATICS
B.E. 1 Year (New) (Common to all Branches) (Main) Examination, June 2011
MATHEMATICS - IY
Time : 3 Hours ] [ Max. Marks : 75
Note : Answer., all questions from Part - A. Answer any five Questions from
Part - B..
PART - A
1.
Eliminate the arbitrary constants from
y = a ex + b e
2
x
and form differential equation.
(Marks 25)
2
2. Solve, (3x
2
+ 2eY)clx + (2xeY + 3y
2
)dy = 0.
3. Show that the set of function x
,-1
k
-
} from series' of the equation
x
2
y" + xy' -y= 0 3
Solve y"
y=
0, y(0) = 0, y'(0)-. 2. 2
Z. Define singular and regular singular points. 2
Show that P
2
-
(u}=
2
-
(3u
2
:- 1)
3
. Find the value 'of
[11
8. Find the solution of the differential equation x
2
y" + Ay
terms of Besselis function:
9. Find Laplace transform df t sinh t.
= 0in
3
2
10. Find inverse Laplace transform of
6 + 2
s
2
- 4s + 3
PART - B (Marks 5 x 10 = 50)
11. (a) Find the integrating factor and hence solve the differential equation
(x
2
+ y
2
) dx- 2xy dy = 0
5
(b) Show that the family of curves
5
v
2
c C+2
+ 1 zr , is self orthogonal.
(This paper contains 2 pages) 1
FirstRanker.com - FirstRanker's Choice
Code No. : 3313/N
FACULTY 01? ENGINEERING & INFORMATICS
B.E. 1 Year (New) (Common to all Branches) (Main) Examination, June 2011
MATHEMATICS - IY
Time : 3 Hours ] [ Max. Marks : 75
Note : Answer., all questions from Part - A. Answer any five Questions from
Part - B..
PART - A
1.
Eliminate the arbitrary constants from
y = a ex + b e
2
x
and form differential equation.
(Marks 25)
2
2. Solve, (3x
2
+ 2eY)clx + (2xeY + 3y
2
)dy = 0.
3. Show that the set of function x
,-1
k
-
} from series' of the equation
x
2
y" + xy' -y= 0 3
Solve y"
y=
0, y(0) = 0, y'(0)-. 2. 2
Z. Define singular and regular singular points. 2
Show that P
2
-
(u}=
2
-
(3u
2
:- 1)
3
. Find the value 'of
[11
8. Find the solution of the differential equation x
2
y" + Ay
terms of Besselis function:
9. Find Laplace transform df t sinh t.
= 0in
3
2
10. Find inverse Laplace transform of
6 + 2
s
2
- 4s + 3
PART - B (Marks 5 x 10 = 50)
11. (a) Find the integrating factor and hence solve the differential equation
(x
2
+ y
2
) dx- 2xy dy = 0
5
(b) Show that the family of curves
5
v
2
c C+2
+ 1 zr , is self orthogonal.
(This paper contains 2 pages) 1
Code No 3313/N
12. (a) Find the general and the singular solution of Clairaut's equation
Y = xY
l
(0
3
.
5
(b) Solve the critical value problem 5
y" + 3y" - 4y = 0, y(0) = 1, y'(0) = 0, y"(0) = 1/2.
13. (a) Find the genei
-
al solution of y" + 3y' + 2y = 2ex. 5
(b) If y. = e'
2
x is the one of the solutions of y" - 6y = 0, find other
solution by reducing the order of the differential equation. 5
14. Find the series solution about x= 0, of the differential equation x(1 + x)y" +
3xyl + y 0. 10
15. (a) Prove that :
(n + 1)p
n
i
4.
i(x).= (2n +
.
1 ) x p
n
(x) 5
(b) Prove that'A(m;14=
22m -1 /3
.
(
rr
i
;
5
16., (a) Express the integral
dx
in terms of
:Gamma functions.
(b) grove that 5
(x).1
= 21
.
1
[j
(x)
? _ 1
2
r
x
2
n
?1
(x)
?
J
1
(x)
?17. (a) Using convolutipn theorem, evaluate 5
L-1 1
?
vs,1)(.+9))
(b) Splve,,
dt2
+ 2 ?
dt,
- 3y = sin t,
d y Lly
5
y =
dt
- 0, when t = 0, using Laplace transform. -
?
2 5,900
FirstRanker.com - FirstRanker's Choice