Download PTU B.Sc (Non-Medical) 2020 March 3rd Sem 76905 Differential Equations Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B.Sc (Non-Medical) 2020 March Previous Question Papers

1 | M-76905 (S105)-1996
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc. (Non Medical) (2018 Batch) (Sem.?3)
DIFFERENTIAL EQUATIONS
Subject Code : BSNM-306-18
M.Code : 76905
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE mark
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Write briefly :
a) Define exact differential equation.
b) What is Clairaut?s equation.
c) Define Cauchy?s linear equation.
d) Define linear differential equation with variable coefficients.
e) Define Partial Differential equation.
f) Form Partial differential equation by eliminating arbitrary constants from the relation
3z = ax
3
+ by
3
.
g) Find general solution of 9r ? 12s + 4t = 0.
h) Write Charpit?s Auxiliary equation.
i) Find general solution of (D
3
? 2D
2
D ?) z = 0.
j) Solve (y ? xp) (p ? 1) = p.

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1 | M-76905 (S105)-1996
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc. (Non Medical) (2018 Batch) (Sem.?3)
DIFFERENTIAL EQUATIONS
Subject Code : BSNM-306-18
M.Code : 76905
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE mark
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Write briefly :
a) Define exact differential equation.
b) What is Clairaut?s equation.
c) Define Cauchy?s linear equation.
d) Define linear differential equation with variable coefficients.
e) Define Partial Differential equation.
f) Form Partial differential equation by eliminating arbitrary constants from the relation
3z = ax
3
+ by
3
.
g) Find general solution of 9r ? 12s + 4t = 0.
h) Write Charpit?s Auxiliary equation.
i) Find general solution of (D
3
? 2D
2
D ?) z = 0.
j) Solve (y ? xp) (p ? 1) = p.

2 | M-76905 (S105)-1996
SECTION-B
2. Solve
3 2
2
1
( ) 0, 0.
3 2 4
y x
y dx x xy dy x
? ?
? ? ? ? ? ?
? ?
? ?

3. Solve the equation y ? ? + a
2
y = sec ax by the method of reduction of order.
4. Find the equation of integral surfaces of (y ? z) p + (z ? x) q = x ? y, which passes through
y = 2x, z = 0
5. Solve by Charpit?s method q = px + q
2

6.
3 2
( 2 ) 3 ( ) ( 2 ) 0
dy dy dy
x y x y y x
dx dx dx
? ? ? ?
? ? ? ? ? ?
? ? ? ?
? ? ? ?


SECTION-C
7. a) Find the orthogonal trajectories of the semi cubical parabolas ay
2
= x
3
, a being the
parameter.
b) Solve
? ?
1
2 2
2
( 1) 2 1
x
D y e
?
?
? ? ? by method of variation of parameter.
8. a) Find the equation of surfaces orthogonal to F (z(x + y)
2
, x
2
? y
2
) = 0
b) Find the general solution of (D
x
3
? 3D
x
2
D
y
+ 4D
y
3
) z = e
x + 2y

9. a) Solve (D
2
? 2D + 4) y = e
x
cos x.
b) Solve the system of equations , 2 3
dx dy
y x y
dt dt
? ? ? ? .



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