Differential equation y/(x^2+y^2)

Click For Summary
SUMMARY

The discussion centers on the differential equation $\frac{dy}{dx}=\frac{y}{x^2+y^2}$. Participants question the correctness of this equation, suggesting it may actually be $\frac{dy}{dx}=\frac{y^2}{x^2+y^2}$, which is homogenous and simplifies the problem. A transformation is proposed, where $x = -\frac{r s'}{s}$ and $y = r$, with $s = s(r)$, to facilitate solving the equation. The conversation emphasizes the importance of clarity in presenting differential equations for effective assistance.

PREREQUISITES
  • Understanding of differential equations and their classifications
  • Familiarity with homogenous functions in calculus
  • Knowledge of variable transformations in solving differential equations
  • Basic proficiency in LaTeX for mathematical notation
NEXT STEPS
  • Study the method of solving homogenous differential equations
  • Learn about variable transformations in differential equations
  • Explore the implications of different forms of differential equations
  • Practice using LaTeX for writing and formatting mathematical expressions
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on differential equations, as well as educators seeking to enhance their teaching methods in this area.

Nikolas7
Messages
22
Reaction score
0
Can you advice the changes in this diff equation:

$\d{y}{x}=\dfrac{y}{x^2+y^2}$
 
Physics news on Phys.org
Hi Nikolas7 and happy new year, :)

We ask that a new question is posted in a new thread rather than tagged at the end of an existing thread (http://mathhelpboards.com/rules/).
That's why I have moved your post to a new thread.

We also ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
Nikolas7 said:
Can you advice the changes in this diff equation:

$\d{y}{x}=\dfrac{y}{x^2+y^2}$

I am wondering if this is the correct DE. Are you sure it's not $\displaystyle \begin{align*} \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{y^2}{x^2 + y^2} \end{align*}$?
 
Prove It said:
I am wondering if this is the correct DE. Are you sure it's not $\displaystyle \begin{align*} \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{y^2}{x^2 + y^2} \end{align*}$?
This would be wonderful if that was true b/c the equation is homogenous. With the right side numerator of power one, the problem is a little more difficult!
 
Make the transformation

$$x = - \dfrac{r s'}{s},\;\;\; y = r$$

where $$s = s(r)$$ and see where that takes you.
 

Similar threads

Undergrad Integral-form change of variable in differential equation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Solving Differential Equation Using Reduction of Order
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Can I Differentiate Both Sides to Solve y in y^2=ln(1-y^2)?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Understanding Legendre differential equation
  • · Replies 2 ·
Replies
2
Views
5K
Undergrad Expressing a differential equation into a different format
  • · Replies 1 ·
Replies
1
Views
2K
MHB Solving a Separable Variable Differential Equation Using U-Substitution
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Determining equilibrium solutions to differential equations
  • · Replies 16 ·
Replies
16
Views
3K
Graduate Volterra equation of the second kind
  • · Replies 1 ·
Replies
1
Views
571
Undergrad Direction Fields and Isoclines
  • · Replies 1 ·
Replies
1
Views
728