# Download VTU BE 2020 Jan Question Paper 17 Scheme 17MAT21 Engineering Mathematics II First And Second Semester

Download Visvesvaraya Technological University (VTU) BE/B.Tech First And Second Semester (1st sem and 2nd sem) 2019-2020 Jan ( Bachelor of Engineering) 17 Scheme 17MAT21 Engineering Mathematics II Previous Question Paper

17MAT21
USN
Second Semester B.E. Degree Examination, Dec.2019/Jan.2020
Engineering Mathematics - II
Time: 3 hrs. Max. Marks: 100
ii
'.--- ..
U
E
71
p
.

,-,
cd
-c,
tu
cl
cri a)
to
d'y dy
... ,
,
1 a. Solve ,
d2y

6 +11---:6y = 0 (06 Marks)
m =
dx' dx - ..dx
'

__ .a :,:.,)
- b. Solve (D
2
- 4)y = Cosh (2x - 1) + 3' (07 Marks)
_o
it
e. S,Olve (D
2
+ 1)y= Secx by the method of variation of parameters. (07 Marks)
_:.o
c
?
E +
NI
P. ,i-
OR
P -
P b
f)

Z
2 a.
Solve D
1
- 9D
2
+23D -15)y = 0 (06 Marks)
.= D
O
b. Solve y" - 4y' + 4y = 8 (Sin2x + x
2
) (07 Marks)
...
?
,--
t?
d
2
y dy ,
c c
_
.- 0

C.
Solve , + 2 ? + 4y = 2x
-
by the method of undetermined coefficients. (07 Marks)
dx
-
dx
8
- ti
,.
Q u
--.- t
Module-2 ? ----
O -0
to
3 a. Solve
(x
2
D
2
+
.--.
.___.
m xi) + 1)y= sin (2logx) (06 Marks)
b. Solve x
2
p
2
+ 3xyp + 2y
-
= 0 (07 Marks)
c '74
45

c. Find the general and singular solution of Clairaut's equation y = xp + p
2
. (07 Marks)
ct =
1
-
,
2

OR
? 7
.
t
.

a
f
,"
? c.. a)
4 a.
Solve (2x + 1)
2
y" - 2 (2x + 1) y' * 12y = 6x (06 Marks)
3 m
_
b. Solve p
2
+ 2py cot x - y
2
7 0 (07 Marks)
0
c
?
'7
.
*

C.
Find the general solution of (p - 1)e
3
x + p
3
e
2Y
= :0 by using the substitution X =ex, Y = e''.
L.. -
,,,, t
4
,
7_,
,

.
(07 Marks)
ct t'
6,
1
,
= 7c
o
>, Li- Module-3
to
c to
5 a. Form the partial differential equation by eliminating the function from
%LI i.
y 7=
(
Z = y-
, 1.
+ 2f + log y (06 Marks)
o I).
c.)
?,
X
o? 2z
i-)Z
b. Solve = sin x siny for which = -2siny when x = 0 and z = 0 when y is an odd
,.,
axay
i
3
Y
0
z
It
multiple of - .
2
(07 Marks)
-
,-- 2
a2u
. c. Derive one dimensional wave e
q
uation
.,

at- ax2
(07 Marks)
Note: Answer any FIVE full questions, choosing
ONE full question from each module.
Module-1
1 of 2
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17MAT21
USN
Second Semester B.E. Degree Examination, Dec.2019/Jan.2020
Engineering Mathematics - II
Time: 3 hrs. Max. Marks: 100
ii
'.--- ..
U
E
71
p
.

,-,
cd
-c,
tu
cl
cri a)
to
d'y dy
... ,
,
1 a. Solve ,
d2y

6 +11---:6y = 0 (06 Marks)
m =
dx' dx - ..dx
'

__ .a :,:.,)
- b. Solve (D
2
- 4)y = Cosh (2x - 1) + 3' (07 Marks)
_o
it
e. S,Olve (D
2
+ 1)y= Secx by the method of variation of parameters. (07 Marks)
_:.o
c
?
E +
NI
P. ,i-
OR
P -
P b
f)

Z
2 a.
Solve D
1
- 9D
2
+23D -15)y = 0 (06 Marks)
.= D
O
b. Solve y" - 4y' + 4y = 8 (Sin2x + x
2
) (07 Marks)
...
?
,--
t?
d
2
y dy ,
c c
_
.- 0

C.
Solve , + 2 ? + 4y = 2x
-
by the method of undetermined coefficients. (07 Marks)
dx
-
dx
8
- ti
,.
Q u
--.- t
Module-2 ? ----
O -0
to
3 a. Solve
(x
2
D
2
+
.--.
.___.
m xi) + 1)y= sin (2logx) (06 Marks)
b. Solve x
2
p
2
+ 3xyp + 2y
-
= 0 (07 Marks)
c '74
45

c. Find the general and singular solution of Clairaut's equation y = xp + p
2
. (07 Marks)
ct =
1
-
,
2

OR
? 7
.
t
.

a
f
,"
? c.. a)
4 a.
Solve (2x + 1)
2
y" - 2 (2x + 1) y' * 12y = 6x (06 Marks)
3 m
_
b. Solve p
2
+ 2py cot x - y
2
7 0 (07 Marks)
0
c
?
'7
.
*

C.
Find the general solution of (p - 1)e
3
x + p
3
e
2Y
= :0 by using the substitution X =ex, Y = e''.
L.. -
,,,, t
4
,
7_,
,

.
(07 Marks)
ct t'
6,
1
,
= 7c
o
>, Li- Module-3
to
c to
5 a. Form the partial differential equation by eliminating the function from
%LI i.
y 7=
(
Z = y-
, 1.
+ 2f + log y (06 Marks)
o I).
c.)
?,
X
o? 2z
i-)Z
b. Solve = sin x siny for which = -2siny when x = 0 and z = 0 when y is an odd
,.,
axay
i
3
Y
0
z
It
multiple of - .
2
(07 Marks)
-
,-- 2
a2u
. c. Derive one dimensional wave e
q
uation
.,

at- ax2
(07 Marks)
Note: Answer any FIVE full questions, choosing
ONE full question from each module.
Module-1
1 of 2
17MAT21
OR
6 a. Form the partial differential equation by eliminating the function from
f(x + y+z, x
.2
+3/
2
+ z
2
) = 0 (06 Marks)
b.
Solve
32
z
-
2
- + z = 0 given that z = cosx and
az
= sin x when y = 0. (07 Marks)
ay ay
2u
c. Obtain the variable separable solution of one dimensional heat equation -- =
, a
?
at ax-
,
(07 Marks)
Module-4
2 2
7 a. Evaluate f f (x
2
+ 3/
2
)dx dy (06 Marks)
01
b.
Evaluate f f
e
dydx by changing the order of integration. (07 Marks)
O x Y
c. Drive the relation between Beta and Gamma function as B(m, n) =
F(m)F(n)
(07 Marks,_
r(m + n)
OR
a
8 a. Evaluate f f(x2 + + )dx dydz (06 Marks)
c b
b.
Find the area between the parabolas y
2
= 4ax and x
2
= 4ay. (07 Marks)
n 2 Tr 2
C. Prove that Sin 0 de
f dO
? (07 Marks)
0
JSinO
Module-5
9
10
a.
b.
c.
a.
b.
Find the Laplace transform of
Express the function f(t) =
Laplace transform.
s + 2
Find L
Cosat Cosbt

in terms of unit step function and
f(t) = t
2
, 0 < t < 2.
1
Laplace transform of , .
(06 Marks)
hence fins,
(07 Marks)
(07 Marks)
(06 Marks)
(07 Marks)
Sint 02

Cost t >
/t

OR
the periodic function
the Inverse
s
-
,
? 2s+5
1

Find the Laplace transform of
Using convolution theorem obtain
3

s (s
-
+ 1)
c. Solve by using Laplace transform y" + 4y' + 4y = et. Given that y(0) = 0, y
1
(0) = 0.
(07 Marks)
2
0
1'
2
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