Use the substitution u(x, y) v(x, y) c(x) and the result of to solve the boundary-value
Chapter 13, Problem 17(choose chapter or problem)
Use the substitution \(u(x, y)=v(x, y)+\psi(x)\) and the result of Problem 16 to solve the boundary-value problem
\(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=-2\), \(0<x<\pi\), \(0<y<\pi\)
u(0, y)=0, \(u(\pi, y)=0\), \(0<y<\pi\)
u(x, 0)=0, \(u(x, \pi)=0\), \(0<x<\pi\)
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