Laplace and differential equation problem.HELP

[rforrevenge]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

I think i have to go backwards starting from H(s) but i don't know how to do it

Any help?

 

[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 $$\frac{d^2f}{dt^2} - \frac{df}{dt}(0^-) - f(0^-)$$.

 

[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.