# Exam2B - 3(10 points For which values of α will the...

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M427K EXAM 2B SPRING, 2008 Dr. Schurle Your name: Your UTEID: Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (10 points) In using our usual method for solving a constant coeﬃcient homogeneous linear diﬀerential equation we are led to an algebraic equation that can be written as ( r - 5) 3 ( r 2 + 8 r + 25) 2 = 0 . What is the general solution of the diﬀerential equation?

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YOUR SCORE: /70 2. (6 points each) (a) Find the general solution of 2 y 00 + y 0 - 6 y = 0 . (b) Find the general solution of 2 y 00 + y 0 - 6 y = 12 e 2 t . (c) What will be the form of a particular solution of 2 y 00 + y 0 - 6 y = 6 te 7 t + 2 cos 5 t ? DO NOT EVALUATE THE COEFFICIENTS!

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Unformatted text preview: 3. (10 points) For which values of α will the solutions of y 00 + 6 y + αy = 0 show oscillatory behavior, that is, behave generally like sin t ? 4. (10 points) Find the general solution of x 2 y 00-3 xy-5 y = 0 on x > 0. 5. (10 points) Given that y 1 = x 2 and y 2 = x 4 are linearly independent solutions of y 00-5 x y + 8 x 2 y = 0 on x > 0, ﬁnd the general solution of y 00-5 x y + 8 x 2 y = x 5 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 00-xy-3 y = 0 , y (0) = 3 , y (0) = 2...
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Exam2B - 3(10 points For which values of α will the...

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