Engineering Board Exam Reviewer · Differential Equations by Laplace Transform · medium

Use Laplace transforms to solve y''-3y'+2y=0 with y(0)=1 and y'(0)=0, and find y(0.5).

1. 3.79
2. 6.02
3. 2.72
4. 0.58

Answer

D. 0.58

Solution

(s2Y-s)-3(sY-1)+2Y=0 Y=s-3/(s-1)(s-2)=2/s-1-1/s-2. So y=2et-e2t and y(0.5)=2e0.5-e 0.58.

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