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8. Consider the system u = y uy= where u(1, y ) = cos(y )
A , xey ,
A= 0 4 3 .
6. Consider the PDE
uyy 4u = sin (xy ) .
(a) Show that A has one eigenvalue, , of multiplicity three with one
Since the partial derivatives with respect1 . Hence absent, this can beof the by
linearly independent eigenvector, v to x are ﬁnd one solution solved
using our understanding of second order ODEs, as follows:
(b) Find two solution u (x, y ) of the associated homogeneous equation u
a) Find the more independent solutions as...
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- Fall '12
- Boundary value problem, general solution