Solve the inital value problem + 14y + 50y = 0, y(0) = 2, y(0) = -17

Answered: y"+ 14y'+ 50y = 0, y(0) = 2, y'(0) =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Solve the inital value problem

Expert Solution

Step 1

Given

$y'' + 14 y' + 50 y = 0$

Initial condition is

$y (0) = 2, y' 0) = - 17$

Auxiliary equation is

$m^{2} + 14 m + 50 = 0 \Rightarrow m = \frac{- 14 \pm \sqrt{14^{2} - 4 \times 50}}{2} \Rightarrow m = \frac{- 14 \pm \sqrt{- 4}}{2} \Rightarrow m = - 7 \pm i$

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