How to manage the absolute value on a differential equation $|T(x)'+A(T,x)+B(T,x)| = f(T,x)$

Hi every person I require to address a formula of this type:

$|T(x)'+A(T,x)+B(T,x)| = f(T,x)$

with borders problems.

The absolute value is my trouble. Certainly without it, the remedy of these is well dealt with in the literary works.

After search in the inquiries I located this:

So, can I do the very same procedure? Or there is an additional means to address this? Many thanks.