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Unformatted text preview: 3. (10 points) For which values of α will the solutions of y 00 + 4 y + αy = 0 show oscillatory behavior, that is, behave generally like sin t ? 4. (10 points) Find the general solution of x 2 y 00 + 5 xy5 y = 0 on x > 0. 5. (10 points) Given that y 1 = x 2 and y 2 = x 3 are linearly independent solutions of y 004 x y + 6 x 2 y = 0 on x > 0, ﬁnd the general solution of y 004 x y + 6 x 2 y = x 2 on x > 0. 6. (12 points) Solve the given initial value problem by means of a power series. Find the recurrence relation, and ﬁnd the ﬁrst four nonzero terms in the solution. y 00xy3 y = 0 , y (0) = 2 , y (0) = 3...
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This note was uploaded on 09/27/2008 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas.
 Spring '08
 Fonken
 Calculus

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