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Part BCSIR NET December 2024the-safe-line-is-where-the-data-vanishes

The safe line is where the data vanishes

The problem has a solution on an open set containing the line { : ax + by = 0} if

  1. A.a = 1 and b = 0
  2. B.a = 1 and b = −1
  3. C.a = 2 and b = 1
  4. D.a = 1 and b = 2

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Related counterexample: A first-order quasilinear Cauchy problem with smooth data has a global smooth solution

More on this topic

The chapter behind this: First-order PDE: characteristics, Lagrange and Charpit — free to read

From Partial Differential EquationsFirst-order PDE: Lagrange, Charpit, characteristics

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