I have a differential equation that goes like this:
$$0.005*\frac{diL}{dt}+iL*2=(0.01-iL)*1$$
And i'm trying to figure out the iL from the equation. I decided to first get rid of the coefficients, and got $$ 0.005*\frac{diL}{dt}+iL*2=(0.01-iL)*1 => 0.005*\frac{diL}{dt}+iL*2=0.01-iL$$ $$\frac{diL}{dt}+iL*2=2-\frac{iL}{0.005} $$ $$ \frac{diL}{dt}+iL=1-100iL$$
From here on, I tried to calculate iL and I ended up with the answer as $$ iL = \frac{1}{100}+\frac{C}{exp(100*t)}$$ And by calculating C, we get $$iL = \frac{1}{100}-\frac{1}{100}*exp(-100*t) $$
I arranged the calculation so that I only had 1 at the right side, as such: $$ \frac{diL}{dt}+100*iL=1 $$ But my calculations seem wrong. Have I done some mistakes along the way, or am I completely off? Value for L is 0.005, if that makes a difference (I dont think it should(?)). The original differential equation is $$L*\frac{diL}{dt}+iL*R1=(Iin-iL)*Rs$$ where I have already input the values for all except iL.
The problem is when you went from the second line to the third. You did not divide the $i_L$ term on the left by $0.005$. I would move that therm to the right, even before I do the division: $$L\frac{di_L}{dt}=I_{in}R_S-i_L(R_s+R_1)$$