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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
Question
Choose the correct answer from the given four option.
Solution of differential equation xdy - ydx = 0 represents:
  1. A rectangular hyperbola.
  2. Parabola whose vertex is at origin.
  3. Straight line passing through origin.
  4. A circle whose centre is at origin.
✓

Answer

  1. Straight line passing through origin.

Solution:

Given that, $\text{xdy}-\text{ydx}=0$

$\Rightarrow\text{xdy}=\text{ydx}$

$\Rightarrow\frac{\text{dy}}{\text{y}}=\frac{\text{dx}}{\text{x}}$

On integrating both sides, we get

$\Rightarrow\int\frac{\text{dy}}{\text{y}}=\int\frac{\text{dx}}{\text{x}}$

$\Rightarrow\log\text{y}=\log\text{x}+\log\text{C}$

$\Rightarrow\log\text{y}=\log\text{Cx}$

$\Rightarrow\text{y}=\text{Cx}$

Which is a straight line passing through origin.

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