differential equation - rectilinear movement of a boat using propulsion I have a problem in my differential equation book that I can't solve because it gives me data that I can't seem to fit in the equation that the book gives me. This is something that I just don't get. Here is the problem : A boat of weight $3000N$ is going from point $0m$ to a point $3500m$ away. The engine of the boat give a propulsion of $140N$ and is helped by an ocean current of $10N$. The resistance of the water is $5Ns/m$ (use $g = 10m/s^2$) I know that this is a rectilinear movement using a proportional resistive force. So \begin{equation*} mv'+bv = -mg. \end{equation*} what I am wondering is how does the $3000N$ weight interacts with the $150N (140+10)$ propulsion... Since we are moving on the $x$ axis does the weight even play a part in this? Also, I do no know the speed at t=0. I only know the position.

Actually I think the equation would be $ma=F-bv$ where a is the acceleration of the boat, $F$ the propulsion force (the 150 N which seems to be constant) and $bv$ the resistive force. You are given $g$ to get the mass of the boat, because what you know it's its weight $p=mg$.