HW5: Problem 9 Previous Problem Problem List Next Problem (1 point) In your answers below, for the variable 1 type the word lambda; for the derivative - 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): luxx + Xuxt - tu = 0 = T'/(t^2T) = 1 . DE for X(x): X'-lambdax^2x = 0 . DE for T(t) : T'-lambdat^2T = 0 (Simplify your answers so that the highest derivative in each equation is positive.) Note: You can earn partial credit on this