Assuming that x1 is the x you mention later, the differential equation is
[tex] y' = b_0+b_1x [/tex]
Since [tex] b_1=0 [/tex], the equation becomes
[tex] y' = b_0 [/tex]
i.e., the derivative is constant. If the derivative is constant, the original function is a line with slope that constant, i.e. the solution of the differential equation is
[tex] y = b_0x+c [/tex]
So, if [tex] b_0>0 [/tex], the line grows when x grows, and so the more you listen, the more bored you are.
If otherwise [tex] b_0<0 [/tex], the line descends when x grows, and so the more you listen, the less bored you are.
Finally, if also [tex] b_0=0 [/tex], then the derivative is constantly zero, which means that the original function is a constant. So, your level of boredom is always the same, no matter how many hours of tutorials you listen to.
