Hi, having difficulty with this D.E. that relates to a tank of initially 400L of pure water, with 1L of salt water (concentration 4g/L) added per min, and 3L of the well-mixed tank solution removed per min. This is what I have so far;

$\displaystyle Q'(t)+\frac{3Q(t)}{400-2t}=4$

I'm trying to find an integrating factor though I keep ending up with a final differentiated x(t) function that doesn't make sense (based on t-200, resulting in the function only existing from t > 200 when it should be from t > 0)

$\displaystyle P(t)=\frac{3}{2(200-t)}$ leading to

$\displaystyle I(t)=-(200-t)^{3/2}$

but then this doesn't seem to make the LHS equal to the derivative of $\displaystyle Q(t)I(t)$? Without the negative sign it would work fine but I'm sure that's the integral of P(t)... a little help? Maybe I've done something stupid...