The differential equation cannot help us in deciding the value of A. It decides only the value
of exponent in the exponential function.
This solution we have arrived at, i.e., Ae
–
α
t
is called the complementary function of
the differential equation in Eqn. 10.4-6 and the differential equation with zero forcing
function is called the homogeneous differential equation.
Now that we have got the function required to enforce compliance with the initial
condition requirement in the circuit, let us proceed to form the total solution for i
L
in series
RL circuit with step input.
(10.4-7)
We evaluate Ato complete the solution by substituting the initial condition ...
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