\[\] \[
\textbf{Q: Solve the equation:} \quad y^2 x^2 \frac{dy}{dx} = x y \frac{dy}{dx}
\]
\[
\textbf{Step 1: Rearranging the equation}
\]
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:
\[
y = \frac{1}{x}
\]