State space representation involving derivatives of input

Set $x_1=y$, $x_2=y'+u$ then \begin{align} x_1'&=y'=x_2-u \\ x_2'&=y''+u'=−7y′−12y−2u\\&=-7(x_2-u)-12x_1-2u\\&=-12x_1-7x_2+5u \end{align}

"Suppose if the physical meaning of $y =$ position and $u =$ force. What is the physical meaning of $x_2$? We know that the $x_1$ will be position, what is the physical meaning of $x_2$? velocity + force? – Unknown123"

You can find a very neat approach here:

https://www.ram.ewi.utwente.nl/aigaion/attachments/single/597

From that it is self-evident that the physical dimension of $y'+u$ comes from the physical dimension of the coefficients of variables.

From the equation $$y′′=−7y′−12y−u′−2u,$$ if $y$ is a length, then $-u'$ and $-2u$ are accelerations, supposed the derivative is with respect to time; in case $u$ is intended to be a force, the coefficient $-2$ should rearrange dimensionality, and its physical meaning is the inverse of a mass. The coefficient of $u'$ has the dimensions of time/mass.