Differential Equation Problem?

In summary, in 1692, Johann Bernoulli taught the Marquis de l'Hopital calculus in Paris. The problem they worked on was finding the equation of a curve with a subtangent equal to twice its abscissa. The subtangent is equal to f(x)/f'(x) and the abscissa is a distance on the x-axis. The equation can be written as f(x)/f'(x) = 2x. A subtangent is a line that touches a curve at one point and has the same slope as the curve at that point.
  • #1
Feldoh
1,342
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?
 
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  • #2
The subtangent is just f(x)/f'(x), isn't it? What's twice the abscissa? Looks like an ODE to me.
 
  • #3
The subtangent is twice the abscissa (which is like a distance on the x-axis?) so...

2f(x)/f'(x) = x?
 
  • #4
Looks more to me like f(x)/f'(x)=2x.
 
  • #5
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:
  • #6
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
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between the rate of change of a dependent variable and the values of one or more independent variables.

2. What are the applications of differential equations?

Differential equations are used in many fields of science and engineering to model and analyze various phenomena, such as population growth, chemical reactions, and electrical circuits.

3. What is the solution to a differential equation problem?

The solution to a differential equation problem is a function that satisfies the equation and its initial or boundary conditions. It can be a closed-form solution, which can be expressed in terms of known mathematical functions, or a numerical solution, which is approximated using computational methods.

4. What are the types of differential equations?

There are several types of differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). ODEs involve only one independent variable, while PDEs involve multiple independent variables. SDEs are used to model systems that involve randomness or uncertainty.

5. How are differential equations solved?

Differential equations can be solved analytically using techniques such as separation of variables, variation of parameters, and Laplace transforms. They can also be solved numerically using methods such as Euler's method, Runge-Kutta methods, and finite difference methods.

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