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

Use Laplace transforms to solve y''+4y= 2t with y(0)=y'(0)=0, and find y≤ft( π4 ).

1. 0.196
2. 0.393
3. 0.785
4. 0.25

Answer

A. 0.196

Solution

s2Y+4Y=s/s2+4 Y=s/(s2+4)2. Since Lt 2t=4s/(s2+4)2, y= 14t 2t. Then y≤ft( π4 )= 14· π4·1= π16 0.196.

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