If we didn't consider friction, this would just be the brachistochrone curve. But what would the optimal path be if there was also a drag force that was in proportion to the object's speed?

The original Brachistochrone problem is without friction and drag. The Brachistochrone problem can also be solved analytically with friction. But what would the optimal path be if there was a drag force that was in proportion to the object's speed?

If we didn't consider friction, this would just be the brachistochrone curve. But what would the optimal path be if there was also a drag force that was in proportion to the object's velocity?

If we didn't consider friction, this would just be the brachistochrone curve. But what would the optimal path be if there was also a drag force that was in proportion to the object's speed?

If we didn't consider friction, this would just be the brachistochrone curve. But what would the optimal path be if there was also a frictional force that was in proportion to the object's velocity?

If we didn't consider friction, this would just be the brachistochrone curve. But what would the optimal path be if there was also a drag force that was in proportion to the object's velocity?