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The singular solution ofis/are
  • a)
    y = ± x2
  • b)
    y = 2x + 3
  • c)
    y = x2 – 2x
  • d)
    y = ± 2x
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The singular solution ofis/area)y = ± x2b)y = 2x + 3c)y = x2&nd...
The given differential equation is

xD2 – 2y D + 4x = 0
The discriminant of this equation is
(-2y)2 – 4x.4x = 0 ⇒ y2 – 4x= 0
Differentiating with respect to x,
⇒ yD = 4x ⇒ D = 4x/y
Substituting D = 4x/y
⇒ y2 – 4x2 = 0
Hence y2 = 4x2 satisfies the given differential equation. The singular solution is
y2 – 4x2 = 0 ⇒ y = ±2x
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