Solution of equation: y 2 x 2 * dy dx xy * dy dx

[latex] \[ \textbf{Q: Solve the equation:} \quad y^2 x^2 \frac{dy}{dx} = x y \frac{dy}{dx} \] \[ \textbf{Step 1: Rearranging the equation} \] We can start by simplifying the equation: \[ y^2 x^2 \frac{dy}{dx} = x y \frac{dy}{dx} \] Cancel \( \frac{dy}{dx} \) from both sides (assuming \( \frac{dy}{dx} \neq 0 \)): \[ y^2 x^2 = x y \] \[ \textbf{Step 2: Simplification} \] Now, divide both sides by \( xy \) (assuming \( x \neq 0 \) and \( y \neq 0 \)): \[ yx = 1 \] \[ \textbf{Step 3: Final Solution} \] Now, solve for \( y \): \[ y = \frac{1}{x} \] \[ \textbf{Final Solution:} \] The solution to the equation is: \[ y = \frac{1}{x} \]