Question

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Find the inverse Laplace transform of F(s), given that (a) lim;+ F(s) = 0; and (b) $F"(s) - F(8) = s-?, 8 >0.

Answer 1

age 1 Solution - we have o of(s) - F(x) = 8 2 870. > F'(A) - 1 Hs) -83 The homogeneous equation looks like F(o) - I F(A)=0. - Integratery, ure get ше a log F/A) - log & s 1 F(s) = s is a homogeneou how to find a particulen solution, het (y - vs. . Ypla v tov! phugging this is , we get Vt srl - 1 vs as-3 ov'=ow a vlas-4 ve -10 3

| Page 2 Tp 3 s3 yp 2 (2) - clearly F(A) = lin sto lin A -1 352 co n in Invees lafface of - 2 - - 1 x Inverse Caplane of - It -lt is the inreese laplace transform:

Solved using different equations with variable coefficients and basic Laplace transforms and inverses.