If y(t) is a solution of the equation ty''+y'+y=0 with y(0) and y'(0) finite, let Y(s)=L|y|(s).
A) Take the laplace transform of the differential equation above to show that Y(s) satisfies the differential equation (s^2+1)Y'(s)+sY(s)=0
B) Solve the differential equation above to find Y(s)
A) Take the laplace transform of the differential equation above to show that Y(s) satisfies the differential equation (s^2+1)Y'(s)+sY(s)=0
B) Solve the differential equation above to find Y(s)