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

Find the differential equation whose general solution is y=C1ex+C2e3x.

  1. y''+4y'+3y=0
  2. y''-3y'+4y=0
  3. y''-4y'+3y=0
  4. y''-4y'-3y=0

Answer

C. y''-4y'+3y=0

Solution

The roots are r=1 and r=3, so the characteristic equation is (r-1)(r-3)=r2-4r+3=0. The differential equation is y''-4y'+3y=0.

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