# d'Alembert's solution

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Consider the wave equation for a semi-infinite string(in the domain x>or =0)

with wave speed c=1, for initial conditions u(x,0)=0 and

(u) subscript (t)(x,0)= (4x)/(1+x^2), x>or =0

Using d'alembert's solution show that the solution of the wave equation for t>or=0

is u(x,t)=In((1+(x+t)^2)/(1+(x-t)^2))

I have to consider the cases x>t and x<t separately.

I know d'Alembert's equation is

u(x,t)=F(x-ct)+G(x+ct)

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The expert considers a wave equation for a semi-infinite string.

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