# Laplace transforms of a reciprocal derivative.

1. Nov 22, 2012

### Locoism

1. The problem statement, all variables and given/known data

The problem basically asks to solve the system

$x'(3x-1)=36e^{6t}$

by using laplace transforms.

3. The attempt at a solution

I've started by writing it

$(3x-1) = \frac{36e^{6t}}{3x-1}$

then applying laplace transform to the left side is quite simple, we get 3X(s) - 1/s.

As for the right hand side, I've fiddled with the identity L[eatf(t)] = F(s-a), I get:

Let $\frac{1}{x'} = f(t)$ then $36L[e^{6t}f(t)]=36F(s-6)$

But then I need to try and find F(s) so that [itex] L^{-1}(F(s)) = \frac{1}{x'} [\itex] and I'm stuck.

What do?