# Laplace of non-homogeneous

## Homework Statement

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

## Homework Equations

i dont 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? im thinking yes but not sure.
also, pretty baffled as to how that gives the original y.

rock.freak667
Homework Helper
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.