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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