Thread: Cauchy-Euler Dif EQ
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Old October 21st, 2007, 12:02 PM
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Quote:
Originally Posted by alikation0 View Post
For a Cauchy Euler Dif EQ, its auxiliary equation for this Dif EQ:

at^2y'' + bty' + cy = g(t) is:

am^2 + (b-a)m + c = 0.

Use this auxiliary equation to solve the Cauchy-Euler equation below:

t^2y'' - 5ty' + 8y = 0 subject to y(2) = 32 and y'(2) = 0
Well, a = 1, b = -5 and c = 8, so the auxiliary equation becomes
m^2 - 6m + 8 = 0

(m - 2)(m - 4) = 0

So m = 2 and m = 4.

Thus the most general solution to this equation is
y = Ax^2 + Bx^4

-Dan
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