The discussion focuses on integrating the ordinary differential equation (ODE) represented by dv/dt = g - kv/m. The integration process involves rewriting the equation as dv/(g - (kv/m)) = dt and applying the substitution method. The final solution derived is gm - kv = Ce^(-kt/m), where C is the constant of integration. This step-by-step guide clarifies the integration process and highlights the importance of substitution in solving ODEs.
PREREQUISITESStudents studying calculus, mathematicians focusing on differential equations, and educators teaching integration techniques will benefit from this discussion.
The left side can be rewritten as ##\frac{m \ dv}{mg - kv}##. There's a fairly obvious substitution you can use.Math10 said:Homework Statement
How to integrate dv/dt=g-kv/m?
Homework Equations
This is ODE.
The Attempt at a Solution
dv/(g-(kv/m))=dt
Now what? I don't know how to integrate the left side.
Math10 said:dv/(g-(kv/m))=dt
Now what? I don't know how to integrate the left side.