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Q44Section B (Part B)44 of 120

d'Alembert solution of the 1-D wave equation

Let u=u(x,t)u=u(x,t) be the solution of

∂2u∂t2−∂2u∂x2=0,x∈R,t>0,u(x,0)=1+x2,∂u∂t(x,0)=x+1.\frac{\partial^2u}{\partial t^2}-\frac{\partial^2u}{\partial x^2}=0, x\in\mathbb R, t>0,\qquad u(x,0)=1+x^2,\qquad \frac{\partial u}{\partial t}(x,0)=x+1.

Then the value of u(1,1)u(1,1) is

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