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Example of the Method of Reduction

Example (cont)

The general solution from the method of reduction is: y(r) = C₁r + C₂/r

Recall that the inner cylinder has radius, a, and the outer cylinder has radius, b. Apply

the boundary conditions.

y(a) = a ω and y(b) = 0

C₁b + C₂/b = 0 and C₁a + C₂/a = a ω

The solution for C₁ and C₂ is:

C₁ = - a² ω/ [ b² - a²]

C₂ = a² b² ω/ [ b² - a²]

y(r) = - a² ω r / [b² - a² ] + a² (b²/r)ω / [b² - a² ]

y(r) = a² ω [ b²/r - r) / [ b² - a² ] (result)