In your answers below, for the variable A type the word lambda; for the derivative 4 X(x) type X' ; for the double derivative X(x) type X"; etc. Separate variables in the following partial...

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Extracted text: In your answers below, for the variable A type the word lambda; for the derivative 4 X(x) type X' ; for the double derivative X(x) type X"; etc. Separate variables in the following partial differential equation for u(x,t): t²uzz + xuz tu = 0 • DE for X(x): = 0 • DE for T(t): = 0 (Simplify your answers so that the highest derivative in each equation is positive.)