Mathematics · Differential Equations
The general solution of Laplace's equation in two dimensions, ∂2u/∂x2 + ∂2u/∂y2 = 0, obtained by separation of variables, is of the form:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1u(x, y) = (c1 cos px + c2 sin px)(c3 cos py + c4 sin py)
- 2u(x, y) = (c1 epx + c2 e-px)(c3 epy + c4 e-py)
- 3u(x, y) = (c1 epx + c2 e-px)(c3 cos py + c4 sin py)✓
- 4u(x, y) = (c1 cos px + c2 sin px)(c3 y + c4)
Correct answer
u(x, y) = (c1 epx + c2 e-px)(c3 cos py + c4 sin py)
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