Download OU B-Tech First Year 2015 June 9356 Faculty Of Engineering Question Paper

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Max. Marks: 75
Note: Answer all questions from Part - A and answer any five questions from Part -B.
PART ? A (25 Marks)
1 Find the values of a and b such that (3ax
2

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+ 2eY)dx + (2bxeY+3y)dy=0 is exact. (2)
2 Obtain the general solution of the Clairaut's equation y = xy' + (y')
3
.
(3)

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3 If yi=e
2x
is a solution of y" ? 5y' + 6y = 0, find the second linearly independent
solution.
(2)

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4 Find a particular integral of (D2-1)y=x4.
(3)
5 Does the differential equation x
3
y"+xy'+y=0 have a Frobenius-series.solution about

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x = 0? Give a reason.
(2)
6 Using Rodrigue's formula, find P2(x).
(3)
7 Define error function. Prove that erf(-x) = -erf(x).

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(2)
8 Evaluate x
4
J
3

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(x)dx in terms of Besse' functions.
(3)
(2)
10 Find the inverse Laplace transform
PART ? B (50 Marks)

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11 (a) Solve (x
3
- 2y
2
)dx + 2xy

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(b) If the temperature of air
g
:is: 0
?
C,:pnd a body cools from 140

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?
C to 80
?
C in
20 minutes, find when the te 'm 'perature will be 35

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?
C.
12 (a) Solve y" y' 6y =
(b) Find the solution of
dy

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the system of equations
1
= y, + y
day',
2

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, - =9y, + y,
di di
13
Find the poweseries solution of the differential equation (1 + x)y" + y' + 3y =0
about x 0.

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14 (a) EVNU4te sin B cos' 0 dO using Beta and Gamma functions.
0

(b) Prove that 1,,
2

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(x)= sin x
Trx
15 (a) Find L{e
-2t
(2 sint ? 4 cosh t)}.

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(b) Solve y" + 2y' ? 3y =0, y(0)=0, y'(0)=4 using Laplace transforms.
16 (a) Find the orthogonal trajectories of the family of curves r
ri
cosn 0=a
n

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, a is the
parameter,
(b) Solve x
3
y"' + 4x

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2
y" + 2xy' ? 2y = 0.
17 (a) Prove that f (x)dx
2/7
2

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+1
(b) Find L
-1

1 }

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using convolution theorem,
9 Find L

(
3

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)
(5)
(
5
)

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(
5
)
(
5

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)
(10)
(
5
)

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(5)
(
5
)
(

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5
)
(
5
)

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(5)
(
5
)
(5)

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