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Section 6.2 Solution of IVP Section 6.2 Solution of I.V.P: Problem 4 Problem 4 User Settings Previous Problem Problem List Next Problem Grades (1 point) Use the Laplace transform to solve the following initial value problem: Problems C y" +by' = 0 y(0) = 2, y'(0) = 1 a. Using Y for the Laplace transform of y(t), i.e., Y = C{y(t)}, find the equation you get by taking the Laplace transform of the differential equation b. Now solve for Y(8) = Problem 1 ✓ Problem 2 v Problemi 3 Problem 4 Problem 5 → Problem 6 Problem 7 Problem 8... Problem 9 v Problem 10 Problem 11 .. Problem 12 Probler 13 A + where a <b o. Write the above answer in its partial fraction decomposition, Y (8) = Y(s) – d. Now by inverting the transform, find (t) - Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor

Answer 1

а бу - 0 with y(o)=2 у'(о)- 1 ху" 3 4 5 6y" } - о sycs) - s yo) - (9) +6 syts) – 6 y(6) = 0

+6sYCS) - 12 0 71 s"ycs) - 25 - 1 = +16+65) YCS) -25-13=0 7 (6765)905= 25+13 7 1Y0- 25+13 5+65 s 25+13 Let. . - 5CS+6) 25+13 = 5 + 556 8 65 ACS+6) + BS 5C5+6) GA=13 comparing At B= 2 B=2-13 =- A = 12 - 5yrs) en GESTO

Yos) 69 - Becom taking Inverse Laplace 7(4) = 2" (+)-da (to) 2-dest ...? - & -c9)] :