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# test2_ans - TEST 2 NO CALCULATORS ‘ MAP 2302 Name 5w...

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Unformatted text preview: TEST 2 (08/07/08) NO CALCULATORS ‘ MAP 2302 Name: 5w ”1‘5 ‘ Summer B 2009 3rd period Section 4787 Please use the blank space and the other side of the sheet to write your solutions, clearly numbering them. 1. (2 pts) Find the radius of convergence of the following series: )Tl °° (-1 2 22727113: 71:0 Note that this power series is a solution of the equation 2. (2 pts) Find ﬁrst two non—zero terms of the Taylor polynomial approximation of the solution of the following initial value problem (write the corresponding Taylor polynomial): y” + ty = 0, y(0)=1, y’(0) = 0 8,70) = ~aaCO) = 0 3"“ 33K- 3"“) 3 3 III a (0): r60: X3 3. (2 pts) Find the recurrence relation for the coefﬁcients m the power series solution of the following equation: y”—9:y'+4y:0 W OWL/p/gac’ise. 4. (2 pts) Determine for each of the following functions whether it is of exponential order. a) f<t>=1n<1+tt b) 90):? Mar MEI) t. m I a 0 A who we Mamie“ Imp”, ‘J/VESK '3 £1)ng “pf =£¢M é’xt’+o:fn:ﬂﬂog Mac 6» +94, 8&6 + ”74*70 0:3":056) 73¢ 80/17? 5. (2pts) . Find the inverse Laplace transform of 1 — —arctan — W. i: =(«/ Uz::(/(e)f :31/‘/((-)]Z§‘)=F/s/ r - - I m. F/s)~ /+SZ 0/64): 9‘ f t 6. (2 pts) Solve the following initial‘value problem using the Laplace transformation: Solve the following integral equation using the Laplace transformation and the convolu— tion theorem ‘rflsz 2.3L. [email protected])=00€f S A; W 8. (2 pts) Find the Laplace transform of the function deﬁned by f(t):t, 0<t<2, 9. (2 pts) Write the reduced order equation used to ﬁnd the second linearly independent solution of the following equation (you don’t have to solve the equation) tzy” — 2253/ ~ 4y : O, t > 0, when you know)! that y1(t)— - — is one solution (Hint: use the substitutzon ,y(t): ”(73.) 3 - . ,m 1 I! 1 3(9) ' {- ‘ 1'? a 262-4 :16 1/".24, +Z4r_ Zv’+%E—ﬂy ' -, ’41., - .4!- t t t a f t 186761 u all “III” '4}! _.£1 20' ’aI'Z'éa ”4-? ‘6”, (“4/0" QM ”I: ’éﬁ ” f e é 1 6 3 f /Mafumea£af¢1&1we damn? J 6 «(L “‘44,; '0 ,I (J l 10. (2 pts) 5% Find 1 * (1 * (1 * (1 * 1))) using the Laplace transformation. >0:me 1 11. -Bonus (2 pts) Find the second linearly independent solution in Problem/F313”: Mic—l ff (6 3!; W the 2W” cm P/mﬂﬁﬂw 9 ‘ ’ M , 5w «(1% M , 6»? WM Mme"; \$0" U/+)= if )m:{ f& mCmd 2W (mﬁ/ﬂﬂuW J’ 5M‘m an): ”(j/Cd {WM/Z (6) £97 ...
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test2_ans - TEST 2 NO CALCULATORS ‘ MAP 2302 Name 5w...

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