Ordinary Differential Equations (ODE) (MATS3107)
Mathematics and Computer Science - MCS
Semester: First Semester
Level: 300
Year: 2017
1
UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE
CONTINUOUS ASSESSMENT
DEPARTMENT: MATHEMATICS COURSE INSTRUCTOR: Tanyu Vivian
MONTH:
April
COURSE CODE & NUMBER:
MATS3107
YEAR:
2017
COURSE TITLE:
Ordinary Differential Equation
DATE:
05/04/2017
CREDIT VALUE:
Six
TI M E ALLO WED:
l hour
I N S T R U C T I O N : A n s w e r a l l t h e q u e s t i o n s . Al l n e c e s s a r y w o r k m u st b e s h o w n a n d m u s t
b e ne a t l y a n d o r d e r ly p r e s e n t e d .
1. i)Define the wronskian of the solution of the ordinary differential equation
y" + P (x) y
'
+ Q (x)y = 0 (1)
ii) Suppose that y
1
and
y
2
are solutions of the equation (1). Prove that the wronskian W (y
1
, y
2
)
is either zero or never zero. (1+ 6marks)
2. Show that y = x and y = x
2
— 1 are linearly independent solutions of the differential equation
(x
2
+ 1)y" — 2xy' + 2y =0
and determine the solution of the non-homogeneous equation
(x
2
+ 1) y" — 2xy' + 2y = 6(x
2
+ 1)
2
(8
-
narks)
GOOD LUCK
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