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

Hint:

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

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.