Differential Equation Problem?

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Homework Help Overview

The problem involves finding the equation of a curve where the subtangent is equal to twice its abscissa. This is situated within the context of differential equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of subtangent and its relation to the curve's properties. There are varying interpretations of the relationship between the subtangent and the abscissa, with some suggesting equations involving derivatives.

Discussion Status

The discussion is active, with participants exploring different interpretations of the subtangent and its mathematical implications. Some guidance has been provided regarding the formulation of the relationship, but no consensus has been reached on the correct approach.

Contextual Notes

Participants express uncertainty about the relevance of the problem to their current studies in differential equations and seek clarification on specific terms like subtangent.

Feldoh
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Homework Statement


In 1692, Johann Bernoulli was teaching the Marquis de l'Hopital calculus in Paris. Solve the following problem, which is similar to the one they did. What is the equation of the curve which has subtangent equal to twice its abscissa.

Homework Equations


None


The Attempt at a Solution


Honestly I'm not really sure where to start. Heck, I'm not even seeing how it's part of the differential equations chapter in my math book. Could anyone just me a push in te right direction?
 
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The subtangent is just f(x)/f'(x), isn't it? What's twice the abscissa? Looks like an ODE to me.
 
The subtangent is twice the abscissa (which is like a distance on the x-axis?) so...

2f(x)/f'(x) = x?
 
Looks more to me like f(x)/f'(x)=2x.
 
Dick said:
Looks more to me like f(x)/f'(x)=2x.

Yeah I just fail at reading XD

Thanks. But I do have one more question what exactly is a subtangent?
 
Last edited:
Feldoh said:
Yeah I just fail at reading XD

Thanks. But I do have one more question what exactly is a subtangent?

I thought YOU knew! I had to google it. http://en.wikipedia.org/wiki/Subtangent
 

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