Mathematics · Partial Differential Equations
Which of the following expressions represents the D'Alembert solution for the wave equation 4uxx - utt = 0, given the initial conditions u(x, 0) = f(x) and ut(x, 0) = g(x)?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1u(x, t) = 12 [g(x+2t) + g(x-2t)]
- 2u(x, t) = 12 [f(x+2t) + f(x-2t)] + 18 ∫x-2tx+2t g(s) ds
- 3u(x, t) = 12 [f(x+2t) + f(x-2t)] + 14 ∫x-2tx+2t g(s) ds✓
- 4u(x, t) = 12 [f(x+2t) + f(x-2t)]
Correct answer
u(x, t) = 12 [f(x+2t) + f(x-2t)] + 14 ∫x-2tx+2t g(s) ds
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