d) Y(x, Solve the equations of part (c) for and, and show that t)=[f(x-at) + f(x + at)].
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- ) Solve the inhomogeneous wave equation on the real lineUtt − c2Uxx = sin x, x ∈ RU(x, 0) = 0, Ut(x, 0) = 0.Explain what theory you are using and show your full computations.Let u=2i-j, v = 5i+j, w = i +5j Find the specified scalar. (4u) v (4u) v =Show whether the following functions are wave functions or not. 1. У(х, t) еxp(ikx) = A- exp (i(ot-Ф)) кЗх3-0313-3kоxt(kx-ot)-iф)) 2 У(х, t) 3. y(x, t) Aexp(i(k³x³-w³t³-3kwxt(kx-wt)-ip)) Аехр (i(-kx? + оt))
- A particle started at A(1,0) circled the origin once an d returned toA(1,0) .what were the change in its coordinatesFind the velocity and acceleration vectors in terms of u, and ug- de r=a cos 20 and dt = 5t, where a is a constant (- 10at sin 20 ) u, + ( 5at cos 20 ) ue y = - a cos (20) • (4 + 5t)) u, + (5a( cos (20) – 4t sin (20)) ue a =2. Find the directional derivative of 9 = yx? +x?z + 3xyz in the direction of vector n = Î + 2ŷ -? .