Choosing the safest initial climbout speed in a twin is a matter of minor controversy.

Some review first. The engines produce a certain fixed amount of energy per unit time during takeoff. This power can be diverted toward some combination of kinetic (airspeed) and potential (altitude) forms, as chosen by the pilot. She makes her choice by choosing an airspeed (or equivalently, an angle of attack for the wings). A low airspeed directs more energy toward the climb, and vice versa. The airplane manual includes standard speeds for maximizing rate and angle of climb on two engines and one. These are roughly the speeds for the Aztec under a standard set of conditions. Generally, optimum operation with one engine is at a slower airspeed than with two. (Similarly, for a single-engined airplane, the best-glide “zero-engine” airspeeds are slower than the normal “one-engine” climb speeds.)

mph	one engine	two engines
best rate	Vyse 102	Vy 120
best angle	Vxse 94	Vx 100

The complete problem scenario is then this. A twin makes a normal two-engined takeoff. Draggy gears and flaps are raised, and a stable climb is established. At some moment early during this climb, one engine fails. The aircraft naturally loses airspeed and climb rate. The pilot recognizes the failure, and responds by adjusting the pitch angle toward the V_yse or V_xse speed, for a sustainable one-engine climb.

The question is what airspeed to choose during this initial climb period. If it’s relatively fast (greater than V_y), then the pilot will have more time available to react before the airplane naturally slows down to V_yse. But the altitude reached by this time will be somewhat smaller. If instead the climb airspeed is kept relatively slow (between V_x and V_y), the airplane may slow below V_xse before the pilot reacts. In this case, a slight dive may be required first to trade altitude for airspeed. But the altitude reached by this time will be higher, making that dive not so bad.

So, which is better to have at the moment of failure? A higher airspeed but lower altitude, so a dive is not needed? Or a lower airspeed but higher altitude, so that a dive is not a problem? I think the issue can be decided generally by considering energy loss during the climb. Consider that some of the engine’s power is lost due to drag, the amount of which increases as a complex function of both airspeed and angle of attack. Whichever option maximizes the total (kinetic + potential) energy of the airplane at the moment of failure is the better one. And since the amount of power produced by the engine is independent of the two options, the only variable source of energy loss is the drag. From various aerodynamics textbooks, drag is lowest near V_y.

This analysis suggests that it’s best to climb at around V_y, in order to maximize energy at the hypothetical moment of failure. The energy difference may not be much though.