# Laplace and differential equation problem.HELP!

1. Dec 5, 2008

### rforrevenge

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

I have this parallel system and i have found its transfer function.Now i have to find what is the differential equation that links the input and the output

2. Relevant equations

u(t)=input, w(t)=output H(s)=w(s)/u(s)=s+1/s(s+1)+1 -->transfer function

3. The attempt at a solution

I think i have to go backwards starting from H(s) but i dont know how to do it

Any help???

2. Dec 5, 2008

### CEL

Multiply w by the denominator and u by the numerator of the TF.
Remember that the inverse transform of sF(s) is $$\frac{df}{dt} - f(0^-)$$ and that of $$s^2F(s)$$ is $$\frac{d^2f}{dt^2} - \frac{df}{dt}(0^-) - f(0^-)$$.

3. Dec 5, 2008

### rforrevenge

Thank you.I did it and i found a DE. Don't know yet if it is correct,though.I will tell you as soon as my teacher grades my paper.Thank for the help,though. I really appreciate it.