Why Is the Differential Equation m*dv/dt = mg - kv^2 Challenging to Solve?

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SUMMARY

The differential equation m*dv/dt = mg - kv² presents significant challenges due to its non-linear nature. The equation describes the motion of an object under the influence of gravity and drag, where m is mass, g is gravitational acceleration, and k is the drag coefficient. A complete solution can be referenced in the Wikipedia article on terminal velocity, which provides insights into the behavior of the system as it approaches steady-state conditions.

PREREQUISITES
  • Understanding of differential equations, particularly first-order non-linear equations.
  • Familiarity with concepts of forces, including gravitational and drag forces.
  • Knowledge of terminal velocity and its implications in physics.
  • Basic calculus skills for manipulating equations and integrating functions.
NEXT STEPS
  • Study the derivation of terminal velocity from the differential equation m*dv/dt = mg - kv².
  • Learn about numerical methods for solving non-linear differential equations.
  • Explore the application of the separation of variables technique in differential equations.
  • Investigate the physical implications of drag coefficients in different mediums.
USEFUL FOR

Students and professionals in physics, engineering, and applied mathematics who are interested in understanding motion under the influence of forces, particularly in contexts involving drag and terminal velocity.

Robert Mak
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m\frac{dv}{dt}= mg - kv^{2}

constants: m, g, k.

I tryed and i can't find a solution to this diferential equation.
 
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m \frac{dv}{dt}=mg-kv^2

\Rightarrow \frac{m}{mg-kv^2} \frac{dv}{dt}=1

\Rightarrow \frac{m}{mg-kv^2} dv=1 dt


Able now?
 
thanks; lol i didnt saw it
 

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