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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
Question
Solution of differential equation x dy - yx = 0 represents:
  1. rectangular hyperbola
  2. straight line passing through origin
  3. parabola whose vertex is at origin
  4. circle whose center is at origin
✓

Answer

  1. straight line passing through origin

Solution:

$=\text{x}\text{ dx}-\text{y}\text{ dx}=0$

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

​Integrating both sides

y = ln x ⇒ y = x

Solution of differential equation

x dy - y x = 0

reperesnts straight line passing through origin

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