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Question

Solution of 2 y sin space x fraction numerator d y over denominator d x end fraction equals 2 sin space x cos space x minus y squared cos space x comma x equals pi over 2 comma y equals 1is given by

  1. y squared equals sin space x
  2. y equals sin squared space x
  3. y squared equals cos space x plus 1
  4. None of these

Hint:

In this question, we will integrate the equation then after putting the value of x and y we will get the value of constant.

The correct answer is: y squared equals sin space x


    G i v e n comma space 2 y sin space x fraction numerator d y over denominator d x end fraction equals 2 sin space x cos space x minus y squared cos space x
rightwards double arrow 2 y sin space x fraction numerator d y over denominator d x end fraction plus y squared cos space x equals sin 2 x
rightwards double arrow 2 sin x fraction numerator d over denominator d x end fraction y squared minus y squared fraction numerator d over denominator d x end fraction sin x equals sin 2 x
rightwards double arrow y squared fraction numerator d over denominator d x end fraction sin x space equals sin 2 x
i n t e g r a t i n g space b o t h space s i d e s comma
integral sin x space y squared space d x space equals integral sin 2 x space d x
rightwards double arrow sin x space y squared equals fraction numerator negative cos 2 x over denominator 2 end fraction plus C
N o w comma space f o r space x equals straight pi over 2 comma space y equals 1
rightwards double arrow sin straight pi over 2.1 squared equals fraction numerator negative cos 2 begin display style straight pi over 2 end style over denominator 2 end fraction plus C
rightwards double arrow C equals 1 plus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses
rightwards double arrow C equals 1 half
sin x. y squared equals fraction numerator negative cos 2 x over denominator 2 end fraction plus 1 half
rightwards double arrow y squared equals fraction numerator 1 minus cos 2 x over denominator 2 sin x end fraction

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