Download OU B-Tech First Year 2013 June 2003 Mathematics II Question Paper

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FACULTY OF ENGINEERING & INFORMATICS
B.E. I-Year (Common to AD) (Main) Examination, June 2013
Subject : Mathematics - II
Time : 3 Hours
Max. Marks: 75

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Note: Answer all questions of Part - A and answer any five questions from Part -B.
PART - A (25 Marks)
1. Form the differential equation by eliminating the arbitrary constant X from
x
2

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+y
2
+2Xx =0.
(2)
2.

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Solve
dy
+
ycosx+siny+y
-0

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(3)
dx sin x + x cos y +x
3. Solve y"-y=0, y(0)=0, y1(0)=2
(3)
4. Find the particular integral of (D

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2
-1)y=8e
3x
(2)
5. Find the Laplace transform of sin 2t sin 3t. (2)

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6. Find the inverse Laplace transform of
2s - 5
(3)
s
2

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4
7. Show that P
n
(1)=1.
(2)

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8. Show that J112(x) =
\
I-
2
sin x

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(3)
gx
9. Evaluate I x
2
e

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-
x'cia-
(2)
n-I
10. Show that f(Iog I dx = 1-(n)

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(3)
0
PART - B (5x10=50 Marks)
11.(a) Solve (3x2y3e4y3+y2)dx+(x3y3eY-xy)dy=0
(5)

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(b) Solve ? -y = y
2
(sinx+cosx).
dy
'

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dx
(
5
)
12.(a) Find the general solution and singular solution of the Clairaut's equation

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Y=xY - (0
3
.
(
5

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)
(b) Solve the initial value problem y"'- 5y"+ 7y' - 3y=0, y(0)=1, y'(0)=0, y"(0)= - 5.
(
5
)

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13.(a) Solve by method of variation of parameters (D
2
+4)y=tan2x.
(b) Solve y"-4y'+13y=12e
2x

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sin3x.
14. Find the series solution about x=0 of the differential equation.
(1 - x
2
)y"-2xy

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1
+2y=0
0 if m#1
-
1

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15.(a) Prove that P
m
(x)P?(x)dx =
2,2+I
(b) Find the Laplace transform of t sin

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2
3t.
/ 16.(a) Apply convolution theorem to evaluate L.
- 1

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.s
(s
2
+ 4)(8
2

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+9)}
28
2
-4
(s +1)(s -2)(s -3)

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17. (a) Show that if -)=
(b) Prove that T
n
+1(2) 2xT
n

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(X)+T
n
_1(X)=0
(b) Find the inverse Laplace transform of
if m=ri

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