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Problem 1.7 Classify the following differential equations as ODEs or PDEs, linear or non-linear, and determine their order. For the linear equations, determine whether or not they are homogeneous. (a) The diffusion equation for u(r, t): 2 u ku, (b) The wave equation for w(r, t): (c) The thin film equation for h(z,t): (d) The forced harmonic oscillator for g(t): (e) The Poisson Equation for the electric potential Ф(x, y,z) : where p(r, y, 2) is a known charge density. (f) Burgers equation for h(r,t):
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