How to apply Laplace transform on a non-homogeneous equation to find y

[brandy]

Homework Statement

do a laplace transform on a given non homogeneous equation.
to eventually find out y

Homework Equations

i don't think the equation is needed. however this non homogeneous equation is equal to Ae^kt

The Attempt at a Solution

well. i applied the laplace to the LHS. with all the '' and ' and stuff. but i didnt incorporate the RHS. can it just be equal to the Laplace of that side? I am thinking yes but not sure.
also, pretty baffled as to how that gives the original y.

 

[rock.freak667]

You'd need to apply the laplace of the RHS.

The LHS would have some function in s multiplied by Y(s).

so

f(s) Y(s) = A/(s-k) as the transform of Ae^kt is A/(s-k)

Y(s) = A/f(s)(s-k)

then you apply the inverse laplace transform on both sides. The LHS becomes y(t), the original y.