Signals and Systems - LTI - Transforms - Impulse Response I have $x(t)-&gt; LTI -&gt; y(t)$ where $LTI=h(t),H(jw)$. 

and 

$H(jw)=ab/((a+jw)(b+jw))$ where a and B are real numbers.

I am wanting to find the impulse response $h(t)$ as well as the input/output differential equation to the system.

If my understanding is correct I would want to take the Fourier transform of the frequency response/input and I am not sure where to go from there.
$$H(jw) = \frac{output}{input} = \frac{Y(jw)}{X(jw)}$$

$$\frac{Y(s)}{X(s)} = \frac{ab}{(a+s)(b+s)}$$

$$s=jw$$

Then you can use some of the notions from this example to solve for your impulse response / differential equation. Hope that helps!