In your answers below, for the variable > type the word lambda; for the derivativeX(x) type X'; for the double derivative Separate variables in the following partial differential equation for u(x, t): x²ut-tut-x²u = 0 (T/(t^2T)) = = 1 DE for X(x): = 0 • DE for T(t): = 0 (Simplify your answers so that the highest derivative in each equation is positive.) X(x) type X"; etc.

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