Answer:
[tex]v_{b}=ir+L\frac{di}{dt}[/tex]
Explanation:
A differential equation that contain a term with di(t)/dt is in a RL circuit. Here we have
[tex]v_{b}=v_{r}+v_{i}[/tex]
where vr is the voltage in the resistance, vi is the voltage in the inductance and vb is the source voltage. But also we have that
[tex]v_{r}=ir\\v_{i}=L\frac{di}{dt}[/tex]
where L is the inductance of the circuit, r is the resistance an i is the current. By replacing we have the differential equation
[tex]v_{b}=ir+L\frac{di}{dt}[/tex]
I hope this is useful for you
regards
