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## Solution (2)

Solution (2)$\left[ x \csc \left( \dfrac{y}{x} \right) - y \right] \, dx + x \, dy = 0$

dy = v dx + x dv

$\left[ x \csc \left( \dfrac{vx}{x} \right) - vx \right] \, dx + x(v \, dx + x \, dv) = 0$

$(x \csc v - vx) \, dx + vx \, dx + x^2 \, dv = 0$

$x \csc v \, dx + x^2 \, dv = 0$

$\dfrac{dx}{x} + \dfrac{dv}{\csc v} = 0$

$\dfrac{dx}{x} + \sin v \, dv = 0$

$\ln x - \cos v = c$

$\ln x - \cos \left(\dfrac{y}{x} \right) = c$

## thanks po sa solution.. yung

thanks po sa solution.. yung prob. 3 and4. po...solution.