The general solution of differential equation $x d y-y d x=0$ represents

The general solution of differential equation $x d y-y d x=0$ represents
  1. the circle whose centre is at the origin
  2. a straight line passing through the origin
  3. a rectangular hyperbola
  4. the parabola whose vertex is at the origin.

Solution

$\begin{aligned} & x d y-y d x=0 \Rightarrow \int \frac{d y}{y}=\int \frac{d x}{x} \\ & \Rightarrow \log y=\log x+\log c \\ & \Rightarrow \log y=\log c x \\ & \Rightarrow y=c x\end{aligned}$ which is a straight line passing through the origin

Asked in: MHT CET 2022 (07 Aug Shift 2)

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