Question

Laplace transform y'' - 6y' + 13y = 0
; y(0)= 0 , y'(0)= -3

Answer 1

so the lapace tranform of y" is\[L(y"(t)) = s^{2}L(y(t)) - sy(0) - y'(0)\]

the laplace transform of y' is\[L(y'(t)) = sL(y(t)) - y(0)\]

Answer 2

those should be given to you

Answer 3

so you should get something like\[s^{2}L(y(t)) +3 -sL(y(t)) -L(y(t)) = 0\]

Answer 4

now just factor out L(y(t)) and solve for L(y(t))