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- Show that f(x, y) =(Aekx + Be-kx )(Ce2ky + De−2ky) is a solution of the wave equation∂2f/∂y2− 4∂2f/∂x2 =0.Solve using wave equation: u(0, t) = u(π, t) = u(x, 0) = 0, du/dt | t = 0 = sin(x)from wave equation ∇2u(r,t) + 1/c2 (∂2u(r,t)/∂t2) = 0, get the Helmholtz equation. Using that u(r,t) = u(r)ei2πνt
- Find the solution to the wave equation on the half - line: utt = c^(2) uxx, x > 0 , t > 0. u(0,t) = 0, t > 0. u(x,0) = 0, ut(x,0) = e^(-2x), x > 0.Find u(x,t) from the wave equation, where length of string is L = 1 , c**2 = 1and the initial velocity is zero and the initial deflection is as follows.Consider the wave equation utt = uxx, (x, t) ∈ R2. find 2 distinct solutions please
- for wave equation, seperation of vairables u(x,t)=X=(x)T(t)For the wave equation in R3(i.e., (x1 , x2 , x3 ) ∈ R3), let u = u(r, t) be theradial symmetric solution of the systemutt = ∆u, 0 ≤ r < ∞, t > 0u(r, 0) = 1, r ≥ 0ut(r, 0) =2, 0 ≤ r ≤ 1,0, r > 1 Find u(2, 1) and u(2, 2).Show that ¥(x,t)= Asin(wt+kx) describes a wave motion
- Use the method of separation of variables to obtain the solution of the wave equation belowsolve the one dimensional wave equation with the boundary conditions and inital conditions as given below: δ2u/δt2 = 1/pi2.δ2u/δx2 u(0,t)= 0, t>0. u(1,t)=0, t>0 u(x,0)= sinππxcosπx, 0<x<1 δu/δt(x,0)=0 0<x<1 using the method of seperation of variable