Maths-
General
Easy

Question

Solution of differential equation d y minus sin space x sin y space d x equals 0 is

  1. e to the power of cos space x end exponent tan space y over 2 equals c
  2. e to the power of cos space x end exponent tan space y equals c
  3. cos space x tan space y equals c
  4. cos space x sin space y equals c

Hint:

In the question we have to integrate the differential equation to find the solution.

The correct answer is: e to the power of cos space x end exponent tan space y over 2 equals c


    G i v e n comma space d y minus sin space x sin y d x equals 0
rightwards double arrow d y equals sin x space sin y space d x
rightwards double arrow fraction numerator d y over denominator d x end fraction fraction numerator 1 over denominator sin y end fraction equals sin x
rightwards double arrow fraction numerator d y over denominator d x space end fraction cos e c y equals sin x space
i n t e g r a t i n g space b o t h space s i d e s
rightwards double arrow log space tan y over 2 plus log space k equals negative cos space x
rightwards double arrow fraction numerator tan begin display style y over 2 end style over denominator C end fraction equals e to the power of negative cos x end exponent
rightwards double arrow e to the power of cos x space tan y over 2 end exponent equals C

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