# What is the solution of y'' + 2y' + 2y = 0, y(0) = 2, y'(0) = -3?

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Find the solution of the initial value problem: y'' + 2y' + 2y = 0, y(0) = 2, y'(0) = -3

Â© BrainMass Inc. brainmass.com March 6, 2023, 12:47 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/linear-algebra-initial-value-problem-16082

#### Solution Preview

Solution. Its characteristic equation is

r^2+2r+2=0

So, r1=-1+i, r2=-1-i

So, y1=e^(-x)sinx y2=e^(-x)cosx ...

#### Solution Summary

A characterisitic equation is found and the initial-value problem is solved.

$2.49