Find the particular solution of the differential equation.
`(dy)/(dx) = ((x sin((x)/(y))-y cos ((x)/(y)))y)/((y cos ((x)/(y))+x sin ((x)/(y)))x)`, given that y = 1 when `x = (pi)/(4)`

Explanation

To find the particular solution of the given differential equation

\[ \frac{dy}{dx} = \frac{(x \sin(\frac{x}{y}) - y \cos(\frac{x}{y})) y}{(y \cos(\frac{x}{y}) + x \sin(\frac{x}{y})) x} \]

given that \( y = 1 \) when \( x = \frac{\pi}{4} \), we will follow these steps:

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