Mathematics · Partial Differential Equations
Let u = u(x, y) be the solution to the following Cauchy problem: u x + u y = e u for (x, y) ∈ ℝ × (0, 1/e) and u(x, 0) = 1 for x ∈ ℝ. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1u y (0, 1/(4e)) = 4e/3✓
- 2u x (1/(4e), 1/(4e)) = log(4)
- 3u x (1/(2e), 1/(2e)) = 0
- 4u(1/(2e), 1/(2e)) = 1
Correct answer
u y (0, 1/(4e)) = 4e/3
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