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- Solve the Goursat problem: = 0 Utt- c²Uxx u|x-ct=0 = x² u/x+ct=0 = x² nt: Use the formula for general solutions of wave equation on the real line. =4. Consider a wave equation on an infinite line, J²u J²u 9 Ət² əx² = 0. = Find the characteristics though the point (1,3). Draw the domains of depen- dence and influence of the point (1,3).) 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.
- Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please use Matlab to solve.The graph of f (θ) = Acos θ + B sin θ is a sinusoidal wave for any constants A and B. Confirm this for (A,B) = (1, 1), (1, 2), and (3, 4) by plotting f .b) A particle moves in simple harmonic motion according to the equation, s = 0 x Acos(wt) + 0 × Bsin(wt), Where s is the displacement, w is the angular d?s + w?s = 0? dt2 frequency and A, B are constant, Show that,