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

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

1. y = C1 e- x/2 + C2 ex
2. y = C1 e2 x + C2 e- x
3. y = C1 ex/2 + C2 e- x
4. y = C1 ex/2 + C2 ex

Answer

C. y = C1 ex/2 + C2 e- x

Solution

2r2+r-1=(2r-1)(r+1)=0 r= 12,-1. Hence y=C1ex/2+C2e-x.

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