Solved: Find the solution of the Dirichlet problem in the upper halfplane that satisfies
Chapter 20, Problem 6(choose chapter or problem)
Find the solution of the Dirichlet problem in the upper half plane that satisfies the boundary condition \(u(x, 0)=\cos x\). [Hint: Let \(s=t-x\) and use the Section 19.6 formulas
\(\int_{-\infty}^{\infty} \frac{\cos s}{s^{2}+a^{2}} d s=\frac{\pi e^{-a}}{a}, \quad \int_{-\infty}^{\infty} \frac{\sin s}{s^{2}+a^{2}} d s=0\)
for \(a>0\).]
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