Part BCSIR NET December 2024the-euler-operator-means-homogeneous

The euler operator means homogeneous

Let u = u(x, y) be the solution of the Cauchy problem $x \partial u / \partial x + y \partial u / \partial y = u, (x, y) \neq = (0, 0)$ , with $u (x, 1) = 1 + x^{2}, x \in R$ . Then which of the following statements is true?

A.u(1, 0) = 0
B. $u (x_{1}, y_{1}) = u (x_{2}, y_{2})$ whenever $x_{1}^{2} + y_{1}^{2} = x_{2}^{2} + y_{2}^{2}$ ✓
C. $u (1, y) = 2$ for all $y \in R$
D. $u (x_{1}, y_{1}) = u (x_{2}, y_{2})$ whenever $x_{1} + y_{1} = x_{2} + y_{2}$

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.

See pricing

50 are analysed free — try those first.

The euler operator means homogeneous

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