5 (3pts). Consider the wave equation ut ur for all -0 < x 0 with the...

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5 (3pts). Consider the wave equation ut ur for all -∞0 < x <∞ and t> 0 with the initial conditions u(x,0) = e-l and u(x,0) = 0. Using the Fourier transform, show that the wave equation has a solution of f(w)etwx cos(ut)dw, where f(u) denotes the Fourier transform of e−1+1, Prove 1 the form u(x, t) 2 cos(wt) cos(wax) 1+w² that this solution also satisfies u(x, t) = -dw. 5 (3pts). Consider the wave equation ut ur for all -∞0 < x <∞ and t> 0 with the initial conditions u(x,0) = e-l and u(x,0) = 0. Using the Fourier transform, show that the wave equation has a solution of f(w)etwx cos(ut)dw, where f(u) denotes the Fourier transform of e−1+1, Prove 1 the form u(x, t) 2 cos(wt) cos(wax) 1+w² that this solution also satisfies u(x, t) = -dw.

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Solution To solve the wave equation we use the Fourier transform to convert the p... View the full answer