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

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Note : Answer., all questions from Part - A. Answer any five Questions from
Part - B..
PART - A
1.
Eliminate the arbitrary constants from

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y = a ex + b e
2
x
and form differential equation.
(Marks 25)

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2
2. Solve, (3x
2
+ 2eY)clx + (2xeY + 3y
2

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)dy = 0.
3. Show that the set of function x
,-1
k
-

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} from series' of the equation
x
2
y" + xy' -y= 0 3
Solve y"

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y=
0, y(0) = 0, y'(0)-. 2. 2
Z. Define singular and regular singular points. 2
Show that P
2

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-
(u}=
2
-
(3u

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2
:- 1)
3
. Find the value 'of
[11

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8. Find the solution of the differential equation x
2
y" + Ay
terms of Besselis function:
9. Find Laplace transform df t sinh t.

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= 0in
3
2
10. Find inverse Laplace transform of
6 + 2

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s
2
- 4s + 3
PART - B (Marks 5 x 10 = 50)
11. (a) Find the integrating factor and hence solve the differential equation

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(x
2
+ y
2
) dx- 2xy dy = 0

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5
(b) Show that the family of curves
5
v
2

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c C+2
+ 1 zr , is self orthogonal.
(This paper contains 2 pages) 1
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Code No. : 3313/N

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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

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Part - B..
PART - A
1.
Eliminate the arbitrary constants from
y = a ex + b e

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2
x
and form differential equation.
(Marks 25)
2

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2. Solve, (3x
2
+ 2eY)clx + (2xeY + 3y
2
)dy = 0.

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3. Show that the set of function x
,-1
k
-
} from series' of the equation

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x
2
y" + xy' -y= 0 3
Solve y"
y=

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0, y(0) = 0, y'(0)-. 2. 2
Z. Define singular and regular singular points. 2
Show that P
2
-

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(u}=
2
-
(3u
2

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:- 1)
3
. Find the value 'of
[11
8. Find the solution of the differential equation x

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2
y" + Ay
terms of Besselis function:
9. Find Laplace transform df t sinh t.
= 0in

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3
2
10. Find inverse Laplace transform of
6 + 2
s

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2
- 4s + 3
PART - B (Marks 5 x 10 = 50)
11. (a) Find the integrating factor and hence solve the differential equation
(x

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2
+ y
2
) dx- 2xy dy = 0
5

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(b) Show that the family of curves
5
v
2
c C+2

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+ 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

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l
(0
3
.
5

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(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

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(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" +

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3xyl + y 0. 10
15. (a) Prove that :
(n + 1)p
n
i

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4.
i(x).= (2n +
.
1 ) x p
n

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(x) 5
(b) Prove that'A(m;14=
22m -1 /3
.
(

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rr
i
;
5
16., (a) Express the integral

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dx
in terms of
:Gamma functions.
(b) grove that 5
(x).1

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= 21
.
1
[j
(x)

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? _ 1
2
r
x
2

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n
?1
(x)
?
J

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1
(x)
?17. (a) Using convolutipn theorem, evaluate 5
L-1 1
?

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vs,1)(.+9))
(b) Splve,,
dt2
+ 2 ?
dt,

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- 3y = sin t,
d y Lly
5
y =
dt

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- 0, when t = 0, using Laplace transform. -
?
2 5,900
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