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Linear PDE, Order, Homogeneous, Non-homogeneous : Boundary Value Problems

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A linear PDE can be written in differential operator notation L(u) = f. where L is the linear differential operator, u is the unknown function, and f is the right-hand side function. For each of the following PDEs, determine the linear operator
and the right-hand side function, the order of the PDE, and whether the PDE is homogeneous or nonhomogeneous:
(a) Uxxx + Uyyy - U = 0
(h) Utt ? Uxx + Uyy + Uzz = xyz
(c) x^2Uxx ? x^2Uy = cos(x) ? sin(y)
(d) y^2Uxx ? x^2Uy = cos(y) ? sin(x)
(e) Ut ? cos(xt)Uxxx ? t^5 = t^2 u

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Solution Summary

Linear PDE, Order, Homogeneous PDE, Non-homogeneous PDE and Boundary Value Problems are investigated.

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