Q72 / 125 · BITSAT 2010 · Mathematics

The solution of differential equation \(2 x \frac{d y}{d x}-y=3\) represents a family of

  • A
    circles
  • B
    straight lines
  • C
    ellipses
  • Correct answer
    D
    parabola

Solution

We have, \(2 x \frac{d y}{d x}=y+3 \Rightarrow \frac{2}{y+3} d y=\frac{d x}{x}\) integrating, \(2 \ln (y+3)=\ln x+\ln c=\ln c x\) \(\Rightarrow \ln (y+3)^2=\ln \mathrm{cx} \Rightarrow(y+3)^2=\mathrm{cx}\) which is a family of parabolas.

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

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