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

Find the general solution of y''+2y'+5y=0.

  1. y = ≤ft(C1 2 x + C2 2 x ) e- x
  2. y = ≤ft(C1 2 x + C2 2 x ) ex
  3. y = ≤ft(C1 5 x + C2 5 x ) e- x
  4. y = ≤ft(C1 x + C2 x ) e- 2 x

Answer

A. y = ≤ft(C1 2 x + C2 2 x ) e- x

Solution

r= -2 (4-20)2=-1 2i, so y=e-x(C1 2x+C2 2x).

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  4. Find the general solution of y''-5y'+6y=0.
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