Find the Laplace transform of y(t) where y is defined by the initial value problem:
y''+18y'+81y=0
y(0)=16
y'(0)=19
Use s as the independent variable for the transformed function.
L(y(t))=?
y''+18y'+81y=0
y(0)=16
y'(0)=19
Use s as the independent variable for the transformed function.
L(y(t))=?
-
Apply L to both sides:
[s^2 L(y(t)) - 16s - 19] + 18 [s L(y(t)) - 16] + 81 L(y(t)) = 0
==> (s^2 + 18s + 81) L(y(t)) - 16s - 307 = 0
==> L(y(t)) = (16s + 307)/(s^2 + 18s + 81).
I hope this helps!
[s^2 L(y(t)) - 16s - 19] + 18 [s L(y(t)) - 16] + 81 L(y(t)) = 0
==> (s^2 + 18s + 81) L(y(t)) - 16s - 307 = 0
==> L(y(t)) = (16s + 307)/(s^2 + 18s + 81).
I hope this helps!