Given two generic functions $x(t)$ and $y(t)$ I want to prove that $x(t) = y(t)$.
To do so, I take the derivative, which turn out to be: $$\dot x(t) = Ax(t) + B$$ $$\dot y(t) = Ay(t) + B$$ where $A$ and $B$ are the same in both derivatives.
Is this sufficient to say both functions are equal?
The reason I ask is that, in general, $x(t)$ and $y(t)$ could have vastly different forms (ie. $x(t)$ could be the resultant of a complicated integral $y(t)$ or something similar). Because of this, I am wondering if I have to go through the trouble of reducing $x(t)$ to $y(t)$ or vice-versa.
Thanks in advance!