Plz answer the Q on successive differentiation?

Question

If (a+bx)(e power (y/x))=x
then show that
(x cube)(second derivative of y)=
[(x)(first derivative of y)-y]whole square

Answer 1

The solution to your question is a bit lengthy and it wont be easy typing that here. However I can tell you the guidelines to arrive at that.
(1)Write down the equation
(2) take differentiation wrt x on both sides.RHS will be 1 here.LHS will have to be diff..you must know how to diff e^(y/x).Use the diff rule for products.
(3) take diff.again of the above obtained equation.you will get alot of terms then.try getting from that the form you want.

Answer 2

e^(y/x)=x/(a+bx)
Take derivative of both sides.

e^(y/x)=e^(1/x * y)

-1/x^2*y+y'*1/x*e^(y/x)=[1*(a+bx)-b*x]/(a+bx)^2
from this equation you can find y'
Then find y''

Replace y' and y'' in the identity to show.