Question

Use the Laplace transform and the procedure outlined in Example 10 to solve the given boundary-value problem. y"2y'y 0 y(O) 6, y(1)6 Need Help?Read It Talk to a Tutor Submit Answer Save ProgressPractice Another Version

Answer 1

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Let y'' + 2y' + y = 0 y' (0) = 6, y (1) = 6 Taking Laplace transform of both sides l {y'' + 2y' + y} = L {0} s^2 L {y (t)} - sy (0) - y' (0) + 2s L {y (t)} - y (0) + L {y (t)} = 0 (s^2 + 2s + 1) L {y (t)] - cs - c - 6 = 0 where c = y (0) L {y (t)} = c (s + 1) + 6/(s^2 + 2s + 1) l {y (t)} = c (s + 1)/(s + 1)^2 + 6/(s + 1)^2 y (t) = C L^-1 {1/(s + 1)} + 6 L^-1 {1/(s + 1)^2} y (t) = c^-et + 6 te^-t Now y (1) = 6 implies c/e + 6/e = 6 implies c + 6 = 6e c = 6e