The slope of the tangent to a curve at any point `(x ,y)` on its given by `y/x-cot(y/x) . cos(y/x) ,(x >0,y >0)` and the curve passes though the point `(1,pi/4)`. Find the equation of the curve.

Explanation

`frac{dy}{dx}=(y/x)-cot(y/x)cos(y/x)`

`frac{dy}{dx}=f(y/x)`

Puting `y=vx`

`frac{dy}{dx}=v+xfrac{dv}{dx}`

`v+xfrac{dv}{dx}=frac{vx}{x}-cotfrac{vx}{x} cosfrac{vx}{x}`

`x frac{dv}{dx}=-cot v cos v`

`frac{dv}{-cot v cos v}=frac{dv}{x}`

`int frac{dv}{-cot v cos v}= int frac{dv}{x}+C`
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