PTU B.Tech CE 2nd Semester May 2019 76254 MATHEMATICS II Question Papers

PTU Punjab Technical University B-Tech May 2019 Question Papers 2nd Semester Civil Engineering (CIV)

Roll No.
Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (Civil) (2018 Batch) (Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-201-18
M.Code : 76254
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION - B & C have FOUR questions each.
3.
Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4.
Select atleast T WO questions from SECT ION - B & C.


SECTION-A
l.
Answer briefly :

a) What is an exact differential equation? Give example.

b) Solve p (1 + q) = qz.

c) Classify the differential equation uxx + uyy = f (x, y).

d) Classify the singular points of x2y + xy + (x2 ? n2) = 0, n is constant.

e) Define ordinary point of a differential equation.

f) Write Laplace equation in spherical coordinates.

g) Show that e?x and xe?x are independent solutions of y + 2y + y = 0 in any interval.

h) Is xux + yuy = u2 a nonlinear partial differential equation?

i) Write an example of linear differential equation of first order.

j) Give an example of elliptic partial differential equation.


SECTION-B
2.
a) The initial value problem governing the current i flowing in a series RL circuit when
di
a voltage v(t) = t is applied, is given by iR L
t, t 0, i (0) = 0, where R and L
dt
are constants. Find the current i (t) at any time t.
(4)

b) Solve (x2D2 + 7xD + 13) y = log (x)
(4)
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3.
a) Solve by the method of variation of parameters y ? 2y + y = ex tan (x).
(4)
2
d y
dy

b) Obtain the series solution of the equation 2
2
x
x
(x 4) y 0.
(4)
2
dx
dx
4.
a) Solve (3D2 ? D)u = sin (2x + 3y).
(4)

b) Find the complete solution of (D3 + D2D ? DD2 ? D3)z = ex cos 2y.
(4)
z

z

5.
a) Solve the partial differential equation (mz ? ny)
(nx lz)
ly mx .
(4)
x

y


b) Find the general solution of partial differential equation :
(4)
2
2
2
z
z
z
4
4

16 log (x 2 y)
2
2
x

x
y

y


SECTION-C
6.
a) Classify the partial differential equation (1 + y2) uxx + (1 + x2)uyy = 0 for different
values of x and y.
(4)
u

u


b) Solve the equation
3
4
,u(0, y) 8 y
e
using method of separation of variables.(4)
x

y

7.
a) Derive D'Alembert's solution of one dimensional wave equation.
(4)

b) Find the deflection of a vibrating string of unit length having fixed ends with initial
velocity zero and initial deflection f(x) = a (x ? x2).
(4)
8.
An insulated rod of length l has its end A and B maintained at 0?C and 100?C,
respectively until steady state conditions prevail. If B is suddenly reduced to 0?C and
maintained at 0?C, find the temperature at a distance x from A at time t.
(8)
2
2
u
u
9.
Solve the Laplace equation

0 subject to the conditions u (0, y) = u (l, y) =
2
2
x
y

(x, 0) = 0 and u (x, a) = sin (nx/l).
(8)

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.

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