Download GTU BE/B.Tech 2019 Winter 1st And 2nd Sem New And Spfu MTH002 Ordinary Differential Equation Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 1st And 2nd Sem New And Spfu MTH002 Ordinary Differential Equation Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? I & II (SPFU) EXAMINATION ? WINTER 2019
Subject Code: MTH002 Date: 07/01/2020

Subject Name: Ordinary Differential Equation
Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:
1. Attempt any five questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Check whether the given differential equation is exact or not
4 2 4 2 3
( 2 ) (2 4 sin ) 0 x xy y dx x y xy y dy ? ? ? ? ? ? .Hence find the general solution.
03
(b) Find the orthogonal trajectories of the family of semi cubical parabolas ay
2
= x
3
04
(c) Solve y
??
-3y
?
+ 2y = e
x
by using variation of Parameter method 07
-
Q.2 (a)
Find the Wronskian of y1,y2 of '' 2 ' log
x
y y y e x ? ? ?
03
(b)
Solve
cos
sin
x
dy
y x e
dx
??
04
(c) Using Method of undetermined Coefficient solve y
?
+ 4y = 8x
2
07

Q.3 (a) Find the orthogonal trajectories of cardioid r = a(1 - cos ? ) 07
(b) Find the Series solution of ' 2 0 y xy ?? 07

Q.4 (a)
Solve
2
'' ' x y xy y x ? ? ?
07
(b) Discuss about Singular point and classify singular pints for the differential
equation
3
( 1) '' 3( 1) ' 7 0 x x y x y xy ? ? ? ? ?

07

Q.5 (a)
Solve in Series the differential equation
2
2
4 2 0
d y dy
xy
dx
dx
? ? ?
07
(b) The population of a country increases at the proportional to the current
population. if the population doubles in 40 years, in how many years will it triple
itself.
07
Q.6 (a)
Solve
2 2 2 2
( 2) (2 ) 0 x y ydx x y xdy ? ? ? ?
07
(b)
Solve
2
( 1)
x
D y xe ?? where D =
d
dx

07

Q.7 (a) Solve the initial value Problem '' 9 0 yy ?? ,y(0) =2, '(0) 1 y ?? 07
(b)
If
1
yx ? is one solution of
2
'' ' 0 x y xy y ? ? ? .Find the second solution
07
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