Mathematics · Partial Differential Equations
Find the solution of the one-dimensional wave equation boundary value problem: 9 uxx = utt, 0 0 u(0, t) = 0 and u(5, t) = 0 u(x, 0) = 4 sin(πx) - sin(2πx) - 3 sin(5πx) ut(x, 0) = 0
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- 1u(x, t) = -4 cos(3πt) sin(πx) - cos(6πt) sin(2πx) - 3 cos(15πt) sin(5πx)
- 2u(x, t) = 4 cos(3πt) sin(πx) - cos(6πt) sin(2πx) + 3 cos(15πt) sin(5πx)
- 3u(x, t) = 4 cos(3πt) sin(πx) + cos(6πt) sin(2πx) - 3 cos(15πt) sin(5πx)
- 4u(x, t) = 4 cos(3πt) sin(πx) - cos(6πt) sin(2πx) - 3 cos(15πt) sin(5πx)✓
Correct answer
u(x, t) = 4 cos(3πt) sin(πx) - cos(6πt) sin(2πx) - 3 cos(15πt) sin(5πx)
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