Final answer:
The question appears to have a typo in the differential equation, preventing a specific solution. Correct methods like separation of variables or integrating factors require a clear equation form, which is not provided. The context hints at a physics problem and implies the use of motion equations.
Step-by-step explanation:
The question appears to contain a typo and may be asking to solve a differential equation. Without the corrected equation, we cannot provide a specific solution. Generally, to solve first-order differential equations, one can use separation of variables, integrating factors, or special techniques for linear differential equations. For example, if we had a correct equation, such as dy/dt = 2yt, we'd use separation of variables by rearranging the terms as dy/y = 2t dt and then integrating both sides. If the equation were linear, we might use an integrating factor. Unfortunately, as presented, dy/dt = 2y₄t₄ty₃ does not convey a clear or correct differential equation format, thus we cannot apply these methods directly. If the equation is meant for a physics context, such as finding the time to the highest point of an object in projectile motion, the correct formula would more likely resemble y = yo + (voy + vy)t, where voy is the initial vertical velocity component, vy is the vertical velocity component at time t, and yo is the initial position, which is often zero.