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Solve the diffusion equation ut=kuxx with the initial condition u(x, 0)=x^2 by the following special method. First show that uxxx satisfies the diffusion equation with zero initial condition. Therefore, by uniqueness, uxxx=0. Integrating this result thrice, obtain u(x,t)= A(t)x^2 + B(t)x+ C(t). Finally it's easy to solve for A, B,.
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