Mathematics · Differential Equations
If a solution of the partial differential equation Uxx + Uyy = 0, 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, with boundary conditions U(x, 0) = U(x, 3) = U(0, y) = U(4, y) = 0 is of the form U(x, y) = (a1eix + a2e−ix)(a3cos(ry) + a4sin(ry)), where a1, a2, a3, a4, r are real constants, then:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The PDE has a non-trivial solution and U(4, 3) = 2
- 2The PDE has a non-trivial solution and U(1, 3) = 0
- 3The PDE has a non-trivial solution and U(4, 1) = 0
- 4The PDE has only the trivial solution✓
Correct answer
The PDE has only the trivial solution
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