pracfin - answer(a The series ∑ ∞ n =1-1 n n a is...

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Practice Final Exam 1. 2.3.7. 2. 4.5.19. 3. 6.3.8. 4. 7.6.27. 5. 8.4.21. 6. 8.6.31. 7. Decide if the following statements are true or false. Explain your answer. (a) We can use the Frobenius to find a power series solution for the equation x 3 y primeprime + 2 xy prime + ( x 5 + e x ) y = 0 about x = 0. (b) It is possible to find two linearly independent solutions for y prime - y = e 2 x . (c) If y 1 and y 2 are two solutions for y 2 ( x ) + y ( x ) + y prime ( x ) = 0, then so is y 1 + y 2 . 8. Decide if the following statements are true or false.
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Unformatted text preview: answer. (a) The series ∑ ∞ n =1 (-1) n n a is always convergent, no matter what pos-itive real number a is. (b) If in a Frobenius equation, we have q ( x ) = e x /x 2 , then 0 is a regular singular point of that equation. (c) If a function is of exponential order, then its Laplacian exists. 1...
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