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

Use Laplace transforms to solve y''+3y'+2y=e-t with y(0)=y'(0)=0, and find y(2).

1. 0.2707
2. 0.1537
3. 0.1353
4. 0.0183

Answer

B. 0.1537

Solution

(s2+3s+2)Y= 1s+1 Y=1/(s+1)2(s+2)=1/(s+1)2-1/s+1+1/s+2. So y=te-t-e-t+e-2t and y(2)=e-2+e-4 0.1537.

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