Download PTU B.Sc CS-IT 2020 March 2nd Sem 71506 Partial Differentiation And Differential Equations Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B-Sc CSE-IT (Bachelor of Science in Computer Science) 2020 March 2nd Sem 71506 Partial Differentiation And Differential Equations Previous Question Paper

1 | M-71506 (S3)-1932

Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc. (CS) (2013 & Onwards) (Sem.?2)
PARTIAL DIFFERENTIATION & DIFFERENTIAL EQUATIONS
Subject Code : BCS-201
M.Code : 71506
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt any FOUR questions.

SECTION-A
1. Answer the following :
a) Define interior point and boundary point.
b) If
2 2
2 2
2
( , )
x y
f x y
x y
?
?
?
then show that
( , ) (0,0)
( , )
x y
Lt f x y
?
does not exist.
c) Discuss the continuity of f (x, y) at (2, 1) where
2 2
2 2
( , ) (0,0)
( , )
0 ( , ) (0,0)
x y
for x y
f x y x y
for x y
? ?
?
?
? ?
?
?
?
?

d) Evaluate
( , ) (1,0)
xy
x y
Lt e
?

e) Define linear differential equation.
f) Define singular solution of a given differential equation.
g) Define homogeneous differential equation.
h) Define orthogonal trajectories.
i) Define separable equation.
j) Define the continuity of a function f (x, y) at a point (a, b).

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1 | M-71506 (S3)-1932

Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc. (CS) (2013 & Onwards) (Sem.?2)
PARTIAL DIFFERENTIATION & DIFFERENTIAL EQUATIONS
Subject Code : BCS-201
M.Code : 71506
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt any FOUR questions.

SECTION-A
1. Answer the following :
a) Define interior point and boundary point.
b) If
2 2
2 2
2
( , )
x y
f x y
x y
?
?
?
then show that
( , ) (0,0)
( , )
x y
Lt f x y
?
does not exist.
c) Discuss the continuity of f (x, y) at (2, 1) where
2 2
2 2
( , ) (0,0)
( , )
0 ( , ) (0,0)
x y
for x y
f x y x y
for x y
? ?
?
?
? ?
?
?
?
?

d) Evaluate
( , ) (1,0)
xy
x y
Lt e
?

e) Define linear differential equation.
f) Define singular solution of a given differential equation.
g) Define homogeneous differential equation.
h) Define orthogonal trajectories.
i) Define separable equation.
j) Define the continuity of a function f (x, y) at a point (a, b).

2 | M-71506 (S3)-1932

SECTION-B
2. State and prove Eulers homogenous theorem.
3. Consider the function
2 2
2 2
2 ( , ) (0,0)
( , )
( , ) (0,0)
x y
for x y
f x y x y
A for x y
?
? ?
?
? ?
?
?
?
?
. Find the value of A
which will make f continuous at origin.
4. If f (x, y) = x
2
ye
y
, then evaluate f
xy
, f
xx
, f
yy
and f
xxx
.
5. Find one parameter family solution of y = px + p
2
, where
dy
p
dx
? .
6. Find the power series solution of
2
2
2
( 1) 3 0
d y dy
x x xy
dx dx
? ? ? ? , about x = 0.
7. Find the solution of Legendre?s equation of order n.












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

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