The differential equation $$a_ny(t)^{(n)} + \dots + a_0y(t)^{(0)} = b_mu(t)^{(m)} + \dots + b_0u(t)^{(0)} $$ with $a_i,b_i \in \mathbb{R}$ and $y,u:\mathbb{R}\to\mathbb{R}$ describes a time-independent, linear, SISO system.
Why is this system noncausal (that means not physically realizable) if $m > n$?
For instance, this equation describes a noncausal system ($n = 0, m = 1$): $$y(t) = u'(t)$$ and using the definition of the derivative it becomes $$y(t) = \lim_{\Delta t \to 0}\frac{u(t + \Delta t) - u(t)}{\Delta t}$$ This means that the output signal at time $t$ depends from a future input signal value $u(t + \Delta t)$ and it makes sense to me that this system is not realizable.
But why this other system is realizable ($n = 1, m = 1$)?
$$y(t) = u'(t) + y'(t)\\\iff$$ $$y(t) = \lim_{\Delta t \to 0}\frac{u(t + \Delta t) - u(t)}{\Delta t} + \lim_{\Delta t \to 0}\frac{y(t + \Delta t) - y(t)}{\Delta t} $$
$y(t)$ depends from a future input signal value too.