Question

Find L^-1 {1/p^2(p^2+1)(p^2+4) }.

Answer 1

(p²+1)(p²+4) / L p²

Hint: Multiply p² +1 and p² +4 together using FOIL.

(p² + 1) (p² + 4) = (p²) (p²) + (p²) (4) + (1) (p²) + (1) (4) = p² + 4p² + p² + 4 = p² +5p² +4:

(p+5 p²+4) / p² L

Roots

p=-i, L#0

p=i, L+0

p=-21, L 0

p=21, L 0