2. (60 points) A function u(r, t) satifies 1 a p2 år 2ди = 1 22u c2 ət2' (1) ar where c is a constant. By introducing th

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2. (60 points) A function u(r, t) satifies 1 a p2 år 2ди = 1 22u c2 ət2' (1) ar where c is a constant. By introducing the new dependent variable vír, t) = ru(r,t), and making the linear coordinate transformation & = r +ct, n= r – ct, reduce this equation to อง = 0. açan Then, show that the general solution u(r, t) has the form u(r, t) = }[s(r + ct) + g(r = ct)); where f and g are arbitrary (twice differentiable) functions.