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Maths-

General

Easy

Question

The solution of the differential equation $left parenthesis 1 plus cos invisible function application x right parenthesis d y equals left parenthesis 1 minus cos invisible function application x right parenthesis d x$ is

$y = 2 \tan \frac{x}{2} - x + c$
$y = 2 \tan x + x + c$
$y = 2 \tan \frac{x}{2} + x + c$
$y = x - 2 \tan \frac{x}{2} + c$

The correct answer is: $y equals 2 tan invisible function application fraction numerator x over denominator 2 end fraction minus x plus c$

Here $fraction numerator d y over denominator d x end fraction equals fraction numerator 1 minus cos invisible function application x over denominator 1 plus cos invisible function application x end fraction equals tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction$ Þ $d y equals open parentheses sec to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction minus 1 close parentheses d x$
Now on integrating both the sides, we get
$y equals 2 tan invisible function application fraction numerator x over denominator 2 end fraction minus x plus c$ .

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