Question: Consider the following partial differential equation Urr + 2kun + khuu = 0, k /0. (a) Classify this equation (order, linearonlinear, homogeneousonhomogeneous, hyper- bolic/parabolic/elliptic); (b)

Consider the following partial differential equation Urr + 2kun + khuu = 0, k /0. (a) Classify this equation (order, linearonlinear, homogeneousonhomogeneous, hyper- bolic/parabolic/elliptic); (b) Find a transformation = r tat, 7 = +bt of the independent variables that transforms the equation into a simpler equation of the form Use = 0. (c) Solve the ordinary differential equation Use = 0 in terms of two arbitrary functions. (d) Using the obtained transformed solution find the solution to the original equation

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