# Solve the general initial value problem modeling the LR circuit, L frac{dI}{dt} + RI=e, I(0)=I_{0} where E is a constant source of emf.

Solve the general initial value problem modeling the LR circuit, where E is a constant source of emf.
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Step 1

Let our equation be where are I - moving charge L - inductor R - resistor E - const First, divide both sides of equation with L
We have first order linear differntial equation. To solve her, we must find integration factor $\mu \left(t\right).$ First, let's define function a(t) We will get integration factor using next formula Now, multiply both sides of our equation with integration factor

Step 2

Integrate both sides of equation