Numerical Methods for Solving Differential Equations

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SUMMARY

This discussion focuses on numerical methods for solving differential equations, specifically addressing the problem of isolating velocity v(t) in the equation involving gravitational force and drag. Participants emphasize the importance of recognizing the equation as separable and suggest moving terms appropriately to facilitate integration. The substitution y=g-(c/m)v is highlighted as a crucial step in the integration process. Additionally, the need for initial conditions is raised, indicating their significance in solving the differential equation accurately.

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  • Understanding of differential equations and their properties
  • Familiarity with integration techniques
  • Knowledge of separable equations in calculus
  • Basic concepts of physics related to forces, such as gravity and drag
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Numerical Methods/Diff Eq :)

2. Problem

2cdizj9.jpg


Clarified: Solving for v(t)

Homework Equations



equation (1)

The Attempt at a Solution



I know the two parts of the hint are important, and tried moving the dt over to the other side and integrating, but I can't seem to isolate the velocity. I think I have to do a derivative before integrating, but I'm not sure how?Thanks guys ;)
 
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Move the g-(c/m)v over to the dv side as well and integrate both sides. The equation is 'separable'. The hint is indicating that you then use the substitution y=g-(c/m)v on the dv side.
 


Dick your answer is incredible, I've also been struggling with differential equations but now it makes a whole lot more sense haha

PS, mr. OP, are there any initial conditions given?
 

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