I have a differential equation $$\frac{d^2y(t)}{dt^2}+y(t) = \frac{dx(t)}{dt} + x^2(t)$$ and I need to see if this system with input $x(t)$ and output $y(t)$ is time invariant and linear. I tried to break up the equation by substituting a linear operator D as the derivative.
So I get: $$y(t) = \frac{Dx(t)+x^2(t)}{D^2 + 1}$$
But the problem is, this equation is meaningless since you are dividing by the derivative operator. However, mathematically, it works out, so can I get $y(t)$ in this form and test for linearity or time invariance using this method?