Laplace Transform of DE

[jjm5119]

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)

 

[royhaas]

A) Use the theorems about Laplace transforms of derivatives.
B) This is a separable equation.

 

[bwat687]

royhaas

I understand what your saying for part B....but could you go into a little more detail about part A and try to show the work for starting the problem?