Signals and Systems - LTI - Transforms - Impulse Response
$$H(jw) = \frac{output}{input} = \frac{Y(jw)}{X(jw)}$$

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

$$s=jw$$

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