1how did you simplify the second term?? i am not getting it !
y= 1+ a1/(x-a1) + a2x/(x-a1)(x-a2) +a3x/(x-a1)(x-a2)(x-a3) +...........upto n+1 terms
if dy/dx = f(x,y) [ a1/(x-a1) + a2/(x-a2) +......... +an/(x-an) then f(x,y)
a. y/x
b. x/y
c. y2/x2
d. x2/y2
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4 Answers
1adding I and II term , x/(x-a1).............(1)
adding (1) and III term, x2/(x-a1)(x-a2)
.
..
...
so 
seperating the terms and simplifying ,
dy/dx=y/x( a1/(x-a1) + ..........)
therefore, f(x,y)=y/x
1first term is 
second term : differentiationis done using chain rule
this can also be written as 
so, the second term is
=
taking xn-1/(∩....) common.. write n as 1+1+1.....(n times).... add 1 to each term.. and then simplify.... u get the ans. [1]