Discussion
Solution of the differential equation
\(xdy - ydx = 0,\)
represents a :
Answer: A
The solution represents a straight line.
Separate the variables:
\[ \begin{aligned} \frac{dy}{y} &= \frac{dx}{x} \\ \log|y| &= \log|x| + C \\ y &= cx \end{aligned} \]
The general solution is the family of straight lines through the origin. (Equivalently, \(x\,dy - y\,dx = 0\) says \(d(y/x) = 0\).) A hyperbola would come from \(x\,dy + y\,dx = 0\), giving \(xy = c\), and a circle from \(x\,dx + y\,dy = 0\).
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