Engineering Board Exam Reviewer · Second-Order Linear Homogeneous Equations · medium

Find the general solution of y''+4y'+4y=0.

1. y = C1 e- 2 x + C2 e2 x
2. y = ≤ft(C1 + C2 x ) e2 x
3. y = C1 2 x + C2 2 x
4. y = ≤ft(C1 + C2 x ) e- 2 x

Answer

D. y = ≤ft(C1 + C2 x ) e- 2 x

Solution

r2+4r+4=(r+2)2=0 gives the repeated root r=-2, so y=(C1+C2x)e-2x.

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