1.
1
2.
2
3.
(a)
(b)
Let a2 = ( x + 1), a1 = x, y1 = x is a solution
By variation of parameters: assume y2 = u ( x) y1 ( x)
u ( x) =
e
a1
a 2 dx
y12
dx =
e
x
x +1 dx
x2
dx =
( x + 1)e ( x +1)
xe x + e x
dx = e 1
dx
x2
x2
= e 1 ( x 1e x + x 2e x )dx
DMA 1275 Engineering Mathematics (I) - Midterm (I)
11/25/2008
1. Derive an expression for the general solution of the given 2nd-order O.D.E.
a2 y ' '+ a1 y '+ a0 y = 0 , if a12 4a0 a2 < 0 .
2. Use the undetermined coefficients approach to find:
(a) y ' '6
