Unformatted text preview: radius of convergence: a) ( x 23) y 00 + 2 xy = 0 b) y 00xyx 2 y = 0 4. Consider the equation x 2 y 00 + x 2 y + y = 0 . Show that: a) x = 0 is a singular point. b) The equation has no nontrivial power series solution of the form y = ∑ ∞ n =0 a n x n . Hint: Show that a n = 0 for all n ≥ . 5. Find the ﬁrst four nonzero terms to the series solution of the equation ( x 24) y 00 + 3 xy + y = 0 , y (0) = 5 , y (0) = 1 . 6. Find a power series solution of the nonhomogeneous equation y 00xy = 1 about the ordinary point x = 0 ....
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 Spring '08
 BEHREND
 Derivative, Power Series, Elementary algebra

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