please try this too

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) +......... +a_n/(x-a_n) then f(x,y)

a. y/x
b. x/y
c. y²/x₂
d. x²/y²

4 Answers

adding 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

how did you simplify the second term?? i am not getting it !

first term is

second term : differentiationis done using chain rule

this can also be written as

so, the second term is

taking x^n-1/(âˆ©....) common.. write n as 1+1+1.....(n times).... add 1 to each term.. and then simplify.... u get the ans. [1]

thank you

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