Differential Equation Problem?

Click For Summary
The discussion centers on a differential equation problem involving the subtangent of a curve being equal to twice its abscissa. Participants express confusion about the problem's connection to differential equations and seek clarification on the concepts of subtangent and abscissa. The subtangent is identified as f(x)/f'(x), leading to the equation f(x)/f'(x) = 2x. There is a request for further explanation of the term "subtangent," indicating a lack of understanding among participants. Overall, the thread highlights the challenges faced in solving the problem and the need for foundational knowledge in calculus concepts.
Feldoh
Messages
1,336
Reaction score
3

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?
 
Physics news on Phys.org
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
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Solve the system of differential equations
  • · Replies 10 ·
Replies
10
Views
2K
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
  • · Replies 7 ·
Replies
7
Views
2K
Simmons 7.10 & 7.11: Find Curves Intersecting at Angle pi/4
  • · Replies 1 ·
Replies
1
Views
2K
Continue solutions of ODEs around the origin
  • · Replies 2 ·
Replies
2
Views
1K
Solving Partial Differential Equation
  • · Replies 2 ·
Replies
2
Views
1K
Solving differential equation (t^2-1)y''-6y=1
  • · Replies 2 ·
Replies
2
Views
901
How can I solve this 2nd degree differential equation?
  • · Replies 2 ·
Replies
2
Views
1K
Use of the constant C in the solution of Differential Equations
  • · Replies 18 ·
Replies
18
Views
4K
Conte Riccati and Jakob Hermann
  • · Replies 3 ·
Replies
3
Views
1K
How do you solve a differential equation with complex numbers?
  • · Replies 3 ·
Replies
3
Views
2K