Question

Find the inverse Laplace transform of the following functions: (i) 3/s + 2/(s - 4), (ii) 2s/(s^2 - 4), (iii) (s + 6)/(s^2 + 4), (iv) 12s/(s^2 - 5s + 6), (v) s^2/((2 + s)^2(3 + s)), (vi) (s - 1)/(s^2 + 6s + 13), (vii) (s + 3)/(s^2 - 4s + 13), (viii) (3s - 5)/((s - 4)(s + 3)), (ix) (s - 4)/((s + 5)(s - 2)), (x) (3s + 16)/(s^2 - 4), (xi) (3s - 2)/((s + 4)(s^2 - s)), (xii) s/(s^2 + 2), (xiii) 1/(s^2 + s - 12), (xiv) 1/(s^3 - 4s), (xv) (s^2 - 6s + 4)/(s^3 - 3s^2 + 2s).

          Find the inverse Laplace transform of the following functions:
(i) 3/s + 2/(s - 4),
(ii) 2s/(s^2 - 4),
(iii) (s + 6)/(s^2 + 4),
(iv) 12s/(s^2 - 5s + 6),
(v) s^2/((2 + s)^2(3 + s)),
(vi) (s - 1)/(s^2 + 6s + 13),
(vii) (s + 3)/(s^2 - 4s + 13),
(viii) (3s - 5)/((s - 4)(s + 3)),
(ix) (s - 4)/((s + 5)(s - 2)),
(x) (3s + 16)/(s^2 - 4),
(xi) (3s - 2)/((s + 4)(s^2 - s)),
(xii) s/(s^2 + 2),
(xiii) 1/(s^2 + s - 12),
(xiv) 1/(s^3 - 4s),
(xv) (s^2 - 6s + 4)/(s^3 - 3s^2 + 2s).

Find the inverse Laplace transform of the following functions:
(i) 3/s + 2/(s - 4),
(ii) 2s/(s^2 - 4),
(iii) (s + 6)/(s^2 + 4),
(iv) 12s/(s^2 - 5s + 6),
(v) s^2/((2 + s)^2(3 + s)),
(vi) (s - 1)/(s^2 + 6s + 13),
(vii) (s + 3)/(s^2 - 4s + 13),
(viii) (3s - 5)/((s - 4)(s + 3)),
(ix) (s - 4)/((s + 5)(s - 2)),
(x) (3s + 16)/(s^2 - 4),
(xi) (3s - 2)/((s + 4)(s^2 - s)),
(xii) s/(s^2 + 2),
(xiii) 1/(s^2 + s - 12),
(xiv) 1/(s^3 - 4s),
(xv) (s^2 - 6s + 4)/(s^3 - 3s^2 + 2s).

Added by Ashley K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/25/2023

Step 1

So, the inverse Laplace transform of 3/(2s + 6) is 3/2 * e^(-3t). (ii) 128/(s^2 + 4) The inverse Laplace transform of 1/(s^2 + a^2) is sin(at). So, the inverse Laplace transform of 128/(s^2 + 4) is 64sin(2t). (iii) 8 - 4s^2/(4s^2 + 82) This function can be Show more…

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Find the inverse Laplace transform of the following functions: (i) 3/(2s + 6) (ii) 128/(s^2 + 4) (iii) 8 - 4s^2/(4s^2 + 82) (iv) (82 - 5s + 6)/(8s - 1) (v) (2 + 8)^2/(3 + s)^2 (vi) (82 + 6s + 13)/(82 - 4s + 13) (vii) (3s - 5)/(s - 4) (viii) (s + 4)/(s + 3)^2 (ix) (s + 5)/(s - 2)^2 (x) 82 - 4/(3s - 2) (xi) (s + 4)/(82 - s)^2 (xii) s^2 + 2/(82 + $12) (xiii) 82 - 6s + 4/(s^2 + 2s) (xiv) s^3 - 4s/(82^3 + 382 + 2s)