Prove that the following inverse of the Laplace transform is true. 2s +13 2s +13 a. L{y}

Prove that the following inverse of the Laplace transform is true.

 

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2s +13 2s +13 a. L{y} = = 9e-7e* 21 -3r s? +5s +6 s° +5s +6 2s b. L{y}= 5 sin 2t +-sint +2 cost 3 s+4(s' +1) (s +1) (s² +1) 1-e* c. L{y}=+1)(s* +4) +L'{s}=sint -sin 21 –() sin(t - 27)+ t. (1)sin(t – 27r) 2s +13 2s +13 a. L{y} = = 9e-7e* 21 -3r s? +5s +6 s° +5s +6 2s b. L{y}= 5 sin 2t +-sint +2 cost 3 s+4(s' +1) (s +1) (s² +1) 1-e* c. L{y}=+1)(s* +4) +L'{s}=sint -sin 21 –() sin(t - 27)+ t. (1)sin(t – 27r)