1. Mathematics
2. Algebra
3. Linear Algebra
4. 10843

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Uxx means second derivative with respect to x
Uyy means second derivative with respect to y

Uxx + Uyy = 0, 0 < x < pi, 0 < y < 1

Ux(0,y) = 0 = U(pi,y), 0 < y < 1

U(x,0) = 1, U(x,1) = 0, 0 < x < pi

Please show all work including how eigenvalues and eigenvectors are derived.
Thank you