# Partial Differential Equations : Separation of Variables (6 Problems)

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11. Separation of Variables. By usingu(x, t) = X(x)T(t) or u(x,y, t) = X(x)Y(y)T(t), separate the following PDEs into two or three ODEs for X and T or X, Y, and T. The parameters c and k are constants. You do not need to solve the equations.

NOTE: one of the equations cannot be separated. Indicate this when you discover that equation.

(a) utt = (xux)x

(b) Utt = C2Uxx

(c) Ut = k(u + Uyy)

(d) ut=k(yu+uy)

(e) Ut + cu ku

(f) Ut = k(yu + XU)

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