Q115 / 180 · KCET 2021 · Mathematics

Solution of differential equating $x d y-y d x=0$ represents

  • A
    A rectangular hyperbola.
  • B
    Parabola whose vertex is at origin.
  • Correct answer
    C
    Straight line passing through origin.
  • D
    A circle whose centre is origin.

Solution

Given, $x d y=y d x$ $\Rightarrow \quad \frac{1}{y} d y=\frac{1}{x} d x$ Integrating both sides, $\begin{aligned} &\quad \int \frac{1}{y} d y=\int \frac{1}{x} d x \\ &\Rightarrow \quad \log y=\log x+\log c \\ &\Rightarrow y=x c \text { which is the equation of line passing } \\ &\text { through origin. } \end{aligned}$

Hence, the correct answer is option: 'C'.

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