Question

solve for u: du/dt = 2(5-u).

Answer 1

\(\int du/(5-u)=\int 2 dt\)
\(-\ln|5-u|=2t+C\)
\(\ln|5-u|=-2t+C\)
\(|5-u|=Ae^{-2t}\) (where \(A\) is just another constant)
\(5-u=\pm Ae^{-2t}\)
\(u=5\pm A e^{-2t}\)