Consider the function z(x, t) that satisfies the PDE vz+625-0 -0 for 20 and t> 0, and the initial condition (z,0) = 0. (a) Apply the Laplace transform in to the PDE and derive an expression for V₂/V. where V(z,s) - L(u(x, t)) is the Laplace transform in t of t. V/ (b) Integrate to find V in the form V(z,s) - C(s)g(z,s), where C(s) comes from the constant of integration and g(0,s) - 1. g(x,s) - 141

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