Solving H.S. Bear's Diff Eq Problem: (1-y^{2}) dx - xy dy = 0

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In summary, the conversation is about reviewing differential equations using H.S. Bear's book and encountering a challenging problem in the variables separate section. The solution given in the book involves using the equation (1-y^{2}) dx - xy dy = 0 and realizing that dx/x = ydy/(1-y^{2}). The person initially had trouble with the problem but eventually solved it with the help of another person.
  • #1
bryanosaurus
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I am reviewing differential equations, going through H.S. Bear's book Diff Eq: Concise Course.
The problem set for the variables separate section were pretty easy and straightforward except for this one, which I can't see how to arrive at the answer given in the book. I'm probably just missing something silly, so maybe another pair of eyes looking at it will clear it up.

(1-y[tex]^{2}[/tex]) dx - xy dy = 0

the solution given is (x[tex]^{2}[/tex])(1-y[tex]^{2}[/tex]) = c
 
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  • #2
Hi bryanosaurus! :smile:
bryanosaurus said:
(1-y[tex]^{2}[/tex]) dx - xy dy = 0

erm … dx/x = ydy/(1 - y²) … ? :smile:
 
  • #3
Okay I got it now, I was fudging a sign when getting rid of the natural logs.
Thanks :)
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is commonly used in physics and engineering to model rates of change or growth in a system.

2. How do you solve a differential equation?

To solve a differential equation, you can use various techniques such as separation of variables, substitution, or integrating factors. These techniques involve manipulating the equation to isolate the dependent variable and then integrating to find the general solution.

3. What is the purpose of solving differential equations?

The purpose of solving differential equations is to find a mathematical model that accurately describes a real-world phenomenon. This allows us to make predictions and understand the behavior of complex systems.

4. How do you know if your solution to a differential equation is correct?

To check the correctness of your solution, you can substitute it back into the original equation and see if it satisfies the equation. You can also use initial or boundary conditions to evaluate the solution.

5. How is this specific differential equation solved?

This specific differential equation, (1-y^{2}) dx - xy dy = 0, can be solved using the substitution method. By substituting u = 1-y^2, the equation can be simplified to a separable form, allowing for the integration and finding the general solution.

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