Find the general circularly symmetric solution to the fourth-order equation 4² (²) =0. E Hint: use plane polar coordinates (p, o), and do not be too eager to expand everything out. Find those circularly symmetric solutions in the unit disc that are equal to unity at the centre p = 0 and vanish on the boundary p = 1. Give a further condition to render the solution unique.

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Chapter2: Second-order Linear Odes
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6. Find the general circularly symmetric solution to the fourth-order equation
4²(²) = 0.
=
Hint: use plane polar coordinates (p, o), and do not be too eager to expand everything out.
Find those circularly symmetric solutions in the unit disc that are equal to unity at the centre
p= 0 and vanish on the boundary p= 1. Give a further condition to render the solution unique.
Transcribed Image Text:6. Find the general circularly symmetric solution to the fourth-order equation 4²(²) = 0. = Hint: use plane polar coordinates (p, o), and do not be too eager to expand everything out. Find those circularly symmetric solutions in the unit disc that are equal to unity at the centre p= 0 and vanish on the boundary p= 1. Give a further condition to render the solution unique.
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