The general solution of x dy dx=y-x tan ⁡ ( yx ) is

Question

Accepted Answer

Correct answer: C. (c) : We are given that x dy dx=y-x tan ⁡ ( yx ) ⇒ dy dx= yx- tan ⁡ ( yx )Clearly, the given differential equation is homogeneous. put y= vx ⇒ dy dx=v+x dv dx ∴v+x dv dx=v- tan ⁡v ⇒x dv dx=- tan ⁡v ⇒ cot ⁡ vdv=- dxx ⇒ log ⁡ sin ⁡v=- log ⁡x+ log ⁡c ⇒ sin ⁡v= cx ⇒ sin ⁡ ( yx )= cx ⇒x sin ⁡ ( yx )=c

$The general solution of x \frac{dy}{dx} = y - x tan (\frac{y}{x}) is$

Solution

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