Solve the following wave equation on the interval [0,T] Utt - c²Uxx = 0, x = [0, π] U(0,t) = 0, U(x,t) = 0 U(x, 0) = 0, Ut(x, 0) = = -12c. cos(x).
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- Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(r) = cos² r are linearly independent on the interval (-x, 0).Find F(s). F(s) = L(1 et + 3e-4t)cos(2t)} -) 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.
- Compute the derivatives of the given functions. d a) dt c) d b) [12 cos ¹2x] dx d) e) f) [5 sin ¹5t] d. du d dz d dy d = dq [4 sec ¹3u] [10 tan-¹2z -1 [6 csc ¹ 4y] [9 cot-¹39] = = = = = G 4- 9- FIThe wave equation describes the motion of a waveform: 0 u/ôt? – d²u/ðx² = 0. Which of the following functions does not satisfy the wave equation? u(x, t) = sin(x)sin(t) u(x, t) = sin(x – t) + cos(x + t) u(x, t) = sin(x – t) u(x, t) = sin(x – t) + cos(x – t) - None of the functions shown.