Part CCSIR NET June 2025the-data-sits-on-a-characteristic-so-it-must-satisfy-the-equation-along-it

The data sits on a characteristic so it must satisfy the equation along it

Consider the Cauchy problem (CP $) x \partial u / \partial x + \partial u / \partial y = 1, u (0, y) = e^{y}, y \in R$ . Then which of the following statements are true?

A.There is NO neighbourhood of the origin on which (CP) has a solution✓
B.(CP) has a unique solution defined on some neighbourhood of the origin
C.(CP) has a unique solution defined on some neighbourhood of the point (0, 1) in the xy-plane
D.(CP) has an infinite number of solutions, each of which is defined on some neighbourhood of the origin

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, and why this one tests hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

The data sits on a characteristic so it must satisfy the equation along it

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