Maths-
General
Easy

Question

Ifx fraction numerator d y over denominator d x end fraction equals y left parenthesis log space y minus log space x plus 1 right parenthesis  then the solution of the equation is:

  1. log space x over y equals c y
  2. log space y over x equals c y
  3. log space x over y equals c x
  4. log y over x equals c x

hintHint:

In this question, we have to find the solution of the equation. For that first we will we separate both x and y and further integrate it and simplify it find the solution.

The correct answer is: log y over x equals c x


    x fraction numerator d y over denominator d x end fraction equals y left parenthesis log space y minus log space x plus 1 right parenthesis
rightwards double arrow fraction numerator d y over denominator d x end fraction equals y over x open parentheses log y over x plus 1 close parentheses
p u t space y equals v x rightwards double arrow fraction numerator d y over denominator d x end fraction equals v plus x fraction numerator d v over denominator d x end fraction
rightwards double arrow v plus x fraction numerator d v over denominator d x end fraction equals v open parentheses log v plus 1 close parentheses
rightwards double arrow fraction numerator d v over denominator v space log space v end fraction equals fraction numerator d x over denominator x end fraction
I n t e g r a t i n g space b o t h space s i d e s comma space w e space g e t colon
rightwards double arrow integral fraction numerator d v over denominator v space log space v end fraction equals integral fraction numerator d x over denominator x end fraction
rightwards double arrow log left parenthesis log space v right parenthesis equals log space x plus log space c
rightwards double arrow log space v equals c x
rightwards double arrow log y over x equals c x

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