Question

Use Laplace transform to solve for the IVP

y''+2y'+y=0, y(0)=1, y'(0)=1

Answer 1

s^2*L-s*y(0)-y'(0)+2sL-2*y(0)+L=0

s^2*L-s-1+2s*L-2+L=0
s^2+2s*L+L=s+3

L[s^2+2s+1]=s+3

L=(s+3)/(s+1)^2

s+3 = A/(s+1) + B/(s+1)^2

s+3 = A(s^2+2s+1)+B(s+1)

s+3 = As^2+(2A+B)s+A+B

2A+B=1
A+B=3

i get A=-2 and B=5 but the book gets A=1 and A=2

idk where i went wrong