How to find the transfer function of xy, xy' etc?

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SUMMARY

The discussion focuses on finding the Laplace transform of the term xy' within the context of the differential equation y'' - xy + y = 1, with initial conditions y(0) = 1 and y'(0) = 2. It is established that xy' does not appear directly in the differential equation, which complicates the process. The Laplace transform can be derived using the formula for t^n f(t) as referenced in the provided Laplace transform table, specifically entry #30, where x is substituted with t, y with f(t), and n is set to 1.

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goggles31
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For example, how would you find the laplace transform of xy' in
y''-xy+y=1, y(0)=1, y'(0)=2 ?
 
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goggles31 said:
For example, how would you find the laplace transform of xy' in
y''-xy+y=1, y(0)=1, y'(0)=2 ?
You don't have xy' in your differential equation.

This table, http://tutorial.math.lamar.edu/pdf/Laplace_Table.pdf, #30, gives the Laplace transform of ##t^n f(t)##. In your problem x = t, y = f(t), and n = 1.
 

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