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(D) Given differential equation is $x \, dy - y \, dx = 0$. Rearranging the terms, we get $x \, dy = y \, dx$. Separating the variables, we have $\fra

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straight line

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(D) Given differential equation is $x \, dy - y \, dx = 0$. Rearranging the terms, we get $x \, dy = y \, dx$. Separating the variables, we have $\frac{dy}{y} = \frac{dx}{x}$. Integrating both sides, we get $\int \frac{dy}{y} = \int \frac{dx}{x} + C$. This results in $\ln|y| = \ln|x| + \ln|c|$, where $\ln|c|$ is the constant of integration. Using logarithmic properties, $\ln|y| = \ln|cx|$, which implies $y = cx$. The equation $y = cx$ represents a straight line passing through the origin.

The solution of the differential equation $x \, dy - y \, dx = 0$ represents a

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