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Maths-

General

Easy

Question

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

$e^{\cos x} \tan \frac{y}{2} = c$
$e^{\cos x} \tan y = c$
$\cos x \tan y = c$
$\cos x \sin y = c$

hint 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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