I have a differential equation that goes like this:

$$ 0,005 * frac {dL} {dt} * iL * 2 = (0,01-iL) * 1 $$

And I try to understand the iL from the equation. I decided to start by getting rid of the coefficients and $$ 0,005 * frac {dL} {d}} iL * 2 = (0,01-iL) * 1 => 0,005 * frac {dL} {d}} iL * 2 = 0,01-iL $$

$$ frac {dL} {dt} * iL * 2 = 2- frac {iL} {0.005} $$

$$ frac {dL} {dt} * iL = 1-100iL $$

From there, I tried to calculate iL and I got the following answer: $$ iL = frac {1} {100} + frac {C} {exp (100 * t)} $$

And by calculating C, we get $$ iL = frac {1} {100} – frac {1} {100} * exp (-100 * t) $$

I arranged the calculation so that I had only 1 on the right, as such:

$$ frac {dL} {dt} + 100 * iL = 1 $$

But my calculations seem wrong. Have I made mistakes along the way or am I completely out of the way?

The value of L is 0.005, if it makes a difference (I do not think it should (?)).

The differential equation of origin is

$$ L * frac {dL} {dt} + iL * R1 = (Iin-iL) * Rs $$

where i've already entered the values for all but iL.