In algebra, one of the most important concepts is Solving partial differential equation.
plug this into the partial differential equation, and ‘compute the derivatives’. Letting u(x,t) = g(x)h(t) in ∂u ∂t − 6 ∂2u ∂x2 = 0 . (18.4) yields ∂ ∂t [g(x)h(t)] − 6 ∂2 ∂x2 [g(x)h(t)] =
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Solving Partial Differential Equation We first look for the general solution of the PDE before applying the initial conditions. Combining the characteristic and compatibility equations, dxds
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