Download VTU ((Visvesvaraya Technological University) B.E/B-Tech 2019 July ( Bachelor of Engineering) First & Second Semester (1st Semester & 2nd Semester) 2018 Jan 2017 Dec I5MAT21 Engineering Mathematics II Question Paper
I5MAT21
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Second Semester B.E. Degree Examination, Dec.2017/Jan.2018
Engineering Mathematics - II
Time: 3 hrs.
Max. Marks: 80
Note: Answer any FIVE full questions, choosing
ONE full question from each module.
Module-1
d
3
y d
2
y 4dy
1 a. Solve + = sinh( 2x + 3) by inverse differential operator method.
dx
--)
dx
dx
(05 Marks)
,
b. Solve
d
2
y 3dy
+ 2y = xe
3x
+- sin 2x by inverse differential operator method. (05 Marks)
dx
2
dx
d y
2
c. Solve + 4y = tan 2x by the method of variation of parameters. (06 Marks)
dx
2
OR
2 a. Solve y" ? 2y' + y = x cos x by inverse differential operator method. (05 Marks)
b. Solve
d2y
+ 4y = x
2
+ 2
?x
+ log 2 by inverse differential operator method. (05 Marks)
dx
2
?x
c. Solve
d2y
+
2dy
+ 4y = 2x
2
4 3e by the method of undetermined coefficients. (06 Marks)
dx
2
dx
Module-2
2
3
3 a. Solve x
3 d Y
+3x
2 d
+ x ?
dY
? y x + log x . (05 Marks)
dx
3
dx
2
dx
b. Solve y ? 2px = tan
-1
(x p
2
) .
(05 Marks)
F lt
c. Solve x
(x 2 +
y 2 ) dY
t xy
` dx dx
(06 Marks)
OR
4 a. Solve (2x + 5)
2
y" ? 6(2x + 5)y' Sy 6x .
(05 Marks)
b. Solve y = 2px + y
2
p
3
(05 Marks)
c. Solve the equation : (px ? y)(py = a
2
p by reducing into Clairaut's form, taking the
substitution X = x2 Y
y
2 = ,
(06 Marks)
1 of 3
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USN
I5MAT21
th
fa.
1E
It
at.)
E
r
b
-
0
-
C
E
O
C
-
c ? -
0
C
-a.
O
o.
r
0
t
O
E
. .
Second Semester B.E. Degree Examination, Dec.2017/Jan.2018
Engineering Mathematics - II
Time: 3 hrs.
Max. Marks: 80
Note: Answer any FIVE full questions, choosing
ONE full question from each module.
Module-1
d
3
y d
2
y 4dy
1 a. Solve + = sinh( 2x + 3) by inverse differential operator method.
dx
--)
dx
dx
(05 Marks)
,
b. Solve
d
2
y 3dy
+ 2y = xe
3x
+- sin 2x by inverse differential operator method. (05 Marks)
dx
2
dx
d y
2
c. Solve + 4y = tan 2x by the method of variation of parameters. (06 Marks)
dx
2
OR
2 a. Solve y" ? 2y' + y = x cos x by inverse differential operator method. (05 Marks)
b. Solve
d2y
+ 4y = x
2
+ 2
?x
+ log 2 by inverse differential operator method. (05 Marks)
dx
2
?x
c. Solve
d2y
+
2dy
+ 4y = 2x
2
4 3e by the method of undetermined coefficients. (06 Marks)
dx
2
dx
Module-2
2
3
3 a. Solve x
3 d Y
+3x
2 d
+ x ?
dY
? y x + log x . (05 Marks)
dx
3
dx
2
dx
b. Solve y ? 2px = tan
-1
(x p
2
) .
(05 Marks)
F lt
c. Solve x
(x 2 +
y 2 ) dY
t xy
` dx dx
(06 Marks)
OR
4 a. Solve (2x + 5)
2
y" ? 6(2x + 5)y' Sy 6x .
(05 Marks)
b. Solve y = 2px + y
2
p
3
(05 Marks)
c. Solve the equation : (px ? y)(py = a
2
p by reducing into Clairaut's form, taking the
substitution X = x2 Y
y
2 = ,
(06 Marks)
1 of 3
15IVIAT:
Module-3
5 a. Obtain- the partial differential equation by eliminating the arbitrary function gig
z yf(X) + x(13.(y)
2
7
b. Solve xy subject to the conditions
az
== log(1 + y) when x .l , and z = 0 when x
(05 Marl
a
u`
2
1
.
1
C.
Derive one dimensional heat equation in the form ?
Qi
= c
2
(06 Marl s)
at ax
OR
(
6
a. Obtain the partial differential equation given f ?z u .
xy ,.,
z
a
2
z
Solve
az
3 ? 4z = 0 subject to the conditions that z = 1 and ?
az
= y when x = 0.
ax
2
ax 5X
(05 Marl
,
s
(05 Marl
(05 Marl- s)
b.
C.
Obtain the solution of one dimensional wave equation
8
2
u 2 a
2
U
= c by the method
ath.
axe
separation of variables for the positive constant. (06 Mart..0
Module-4
b.
(05 Marl,
(05 Maas
x
2 2
Find the area of the ellipse ? 1 by double integration.
a b
a
=
2
N
F
a
2
x
7
a.
Evaluate I = sx
y
zdzd
y
dx .
0 0 0
c.
Derive the relation between beta and gamma function as f3(m, n
F(m)F(n)
. (06 Marl
r(M + n)
OR
a
r
x dx dy
8 a. Evaluate by changing the order of integration.
2 2
(05 Marl N;
o
y
x +y
a
V
ia' ?y
2
b Evaluate j yj(
2
+ y' dx dy by changing into polar co-ordinates. (Os Marl, g
0 0
it/
IC
c.
Evaluate
d0
---x f,/sin 0 de by using Beta-Gamma functions. (06 Marl,
sin 0
0
2 of 3
FirstRanker.com - FirstRanker's Choice
USN
I5MAT21
th
fa.
1E
It
at.)
E
r
b
-
0
-
C
E
O
C
-
c ? -
0
C
-a.
O
o.
r
0
t
O
E
. .
Second Semester B.E. Degree Examination, Dec.2017/Jan.2018
Engineering Mathematics - II
Time: 3 hrs.
Max. Marks: 80
Note: Answer any FIVE full questions, choosing
ONE full question from each module.
Module-1
d
3
y d
2
y 4dy
1 a. Solve + = sinh( 2x + 3) by inverse differential operator method.
dx
--)
dx
dx
(05 Marks)
,
b. Solve
d
2
y 3dy
+ 2y = xe
3x
+- sin 2x by inverse differential operator method. (05 Marks)
dx
2
dx
d y
2
c. Solve + 4y = tan 2x by the method of variation of parameters. (06 Marks)
dx
2
OR
2 a. Solve y" ? 2y' + y = x cos x by inverse differential operator method. (05 Marks)
b. Solve
d2y
+ 4y = x
2
+ 2
?x
+ log 2 by inverse differential operator method. (05 Marks)
dx
2
?x
c. Solve
d2y
+
2dy
+ 4y = 2x
2
4 3e by the method of undetermined coefficients. (06 Marks)
dx
2
dx
Module-2
2
3
3 a. Solve x
3 d Y
+3x
2 d
+ x ?
dY
? y x + log x . (05 Marks)
dx
3
dx
2
dx
b. Solve y ? 2px = tan
-1
(x p
2
) .
(05 Marks)
F lt
c. Solve x
(x 2 +
y 2 ) dY
t xy
` dx dx
(06 Marks)
OR
4 a. Solve (2x + 5)
2
y" ? 6(2x + 5)y' Sy 6x .
(05 Marks)
b. Solve y = 2px + y
2
p
3
(05 Marks)
c. Solve the equation : (px ? y)(py = a
2
p by reducing into Clairaut's form, taking the
substitution X = x2 Y
y
2 = ,
(06 Marks)
1 of 3
15IVIAT:
Module-3
5 a. Obtain- the partial differential equation by eliminating the arbitrary function gig
z yf(X) + x(13.(y)
2
7
b. Solve xy subject to the conditions
az
== log(1 + y) when x .l , and z = 0 when x
(05 Marl
a
u`
2
1
.
1
C.
Derive one dimensional heat equation in the form ?
Qi
= c
2
(06 Marl s)
at ax
OR
(
6
a. Obtain the partial differential equation given f ?z u .
xy ,.,
z
a
2
z
Solve
az
3 ? 4z = 0 subject to the conditions that z = 1 and ?
az
= y when x = 0.
ax
2
ax 5X
(05 Marl
,
s
(05 Marl
(05 Marl- s)
b.
C.
Obtain the solution of one dimensional wave equation
8
2
u 2 a
2
U
= c by the method
ath.
axe
separation of variables for the positive constant. (06 Mart..0
Module-4
b.
(05 Marl,
(05 Maas
x
2 2
Find the area of the ellipse ? 1 by double integration.
a b
a
=
2
N
F
a
2
x
7
a.
Evaluate I = sx
y
zdzd
y
dx .
0 0 0
c.
Derive the relation between beta and gamma function as f3(m, n
F(m)F(n)
. (06 Marl
r(M + n)
OR
a
r
x dx dy
8 a. Evaluate by changing the order of integration.
2 2
(05 Marl N;
o
y
x +y
a
V
ia' ?y
2
b Evaluate j yj(
2
+ y' dx dy by changing into polar co-ordinates. (Os Marl, g
0 0
it/
IC
c.
Evaluate
d0
---x f,/sin 0 de by using Beta-Gamma functions. (06 Marl,
sin 0
0
2 of 3
15MAT21
Module-5
9 a.
Find the Laplace transform of t-2
cos 2t -cos3t
+ t sin t . (05 Marks)
t, 0 < t < TC
b. Express the function f(t) = in terms of unit step function and hence find
sin t, t >
its Laplace transform. (05 Marks)
C. Solve y" + 6y' +9y
-
- '
t -3t
subject to the conditions, y(0)
,
0 = y'(0) by using Laplace
transform. (06 Marks)
OR
10 a.
Find he inverse Laplace form of
7s + 4
(05 Marks)
4s
-
+ 4s + 9
b. Find the Laplace transform of the full wave rectifier f(t) = E sin cot, 0 < t < Tt/to having
period 7t/to. (05 Marks)
C. Obtain the inverse Laplace transform of the function
1
by using convolution
(s -1)(s
2
+1)
theorem. (06 Marks)
3 of3
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This post was last modified on 01 January 2020