Mathematics · Partial Differential Equations
The solution of the partial differential equation ∂2u∂t2 - ∂2u∂x2 = 0 satisfying the boundary conditions u(0,t) = 0 = u(L,t) and initial conditions u(x,0) = sin(πx/L) and ∂u∂t|t=0 = sin(2πx/L) is:
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- 1sin(πx/L) cos(πt/L) + L2π sin(2πx/L) cos(2πt/L)
- 22 sin(πx/L) cos(πt/L) - sin(πx/L) cos(2πt/L)
- 3sin(πx/L) cos(2πt/L) + Lπ sin(2πx/L) sin(πt/L)
- 4sin(πx/L) cos(πt/L) + L2π sin(2πx/L) sin(2πt/L)✓
Correct answer
sin(πx/L) cos(πt/L) + L2π sin(2πx/L) sin(2πt/L)
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