Mathematics · Partial Differential Equations
Let p ∈ R. Consider the partial differential equation ∂2u/∂x2 + ∂2u/∂y2 = 0. Which of the following CANNOT be a solution to this PDE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1u(x, y) = (c1x + c2)(c3y + c4)
- 2u(x, y) = (c1epx + c2e-px)(c3cos(py) + c4sin(py))
- 3u(x, y) = (c1cos(px) + c2sin(px))(c3epy + c4e-py)
- 4u(x, y) = (c1x2 + c2x + c3)(c4y + 1)✓
Correct answer
u(x, y) = (c1x2 + c2x + c3)(c4y + 1)
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