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5. Given y = ciet cos(t) + czet sin(t) is a family of solutions of y" + 2y' + 2y = 0. Find a solution of the second-order IVP (initial-value problem) consisting of this differential equation and the following initial conditions. (a) y(0) = 0, y/(0) = 0 1. (b) y(0) = 2, y' (0) %3D

5. Given y = ciet cos(t) + czet sin(t) is a family of solutions of y" + 2y' + 2y = 0. Find a solution of the second-order IVP (initial-value problem) consisting of this differential equation and the following initial conditions. (a) y(0) = 0, y/(0) = 0 1. (b) y(0) = 2, y' (0) %3D

Advanced Engineering Mathematics
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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my question is in the image.

I did try to solve this but I think I did it wrong as for part a I got c1=0 and c2=0. for part b I got that c1=2 and that c2=-1/2. Both of these seem off. Can you please help me?

5. Given y = ciet cos(t) + czet sin(t) is a family of solutions of y" + 2y' + 2y = 0. Find a solution of the second-order IVP (initial-value problem) consisting of this differential equation and the following initial conditions. (a) y(0) = 0, y/(0) = 0 1. (b) y(0) = 2, y' (0) %3D
Transcribed Image Text:5. Given y = ciet cos(t) + czet sin(t) is a family of solutions of y" + 2y' + 2y = 0. Find a solution of the second-order IVP (initial-value problem) consisting of this differential equation and the following initial conditions. (a) y(0) = 0, y/(0) = 0 1. (b) y(0) = 2, y' (0) %3D
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