For the differential equations, find the particular solution satisfying the given condition: \[ \bigg[ x \: sin^2 \bigg( \frac{x}{y} - y \bigg) \bigg] dx + xdy = 0; y \frac{\large \pi}{\large 4} when \: x = 1\]

Question

$\begin{array}{1 1}\cot \large(\large\frac{y}{x}) = \log \left | ex \right | \\ \cot \large(\large\frac{x}{y}) = \log \left | ex \right | \\ \tan \large(\large\frac{y}{x})= \log \left | ex \right | \\\cos \large(\large\frac{y}{x}) = \log \left | ex \right | \end{array} $