Question

what is the laplace of the differential equation:
y''+6y'+10y=g(t) y(0)=-4, y'(0)=3

Answer 1

all you need to know here is\[\mathcal L\{y''(t)\}=s^2Y(s)-sy(0)-y'(0)\]\[\mathcal L\{y'(t)\}=sY(s)-y(0)\]\[\mathcal L\{y(t)\}=Y(s)\]and\[\mathcal L\{g(t)\}=G(s)\]just use a table!
http://tutorial.math.lamar.edu/Classes/DE/Laplace_Table.aspx