Need help to solve y'=(x^2+y^2)^(3/2)

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Discussion Overview

The discussion revolves around solving the differential equation y'=(x^2+y^2)^(3/2). Participants explore various methods and transformations to approach the problem, including coordinate transformations and the chain rule.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant requests help to solve the equation and expresses uncertainty about the correct approach.
  • Another participant suggests that the thread should follow a specific template for homework help, emphasizing the need for a clear problem statement and previous attempts at a solution.
  • A participant proposes using a coordinate transformation where x^2+y^2=r^2 and expresses confusion about how to compute dy/dx in this context.
  • Some participants discuss using the chain rule to relate dy/dx to dy/dr and dr/dx, noting that this approach becomes complicated.
  • One participant mentions that their attempt with the chain rule leads to a new problem involving r^3 and suggests developing a new equation of a circle to make the problem solvable.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method to solve the equation, and multiple approaches are proposed without resolution.

Contextual Notes

There are unresolved mathematical steps and dependencies on the chosen coordinate transformation, which may affect the clarity of the solution process.

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i need some help to solve this equation..

[tex]\frac{dy}{dx}=(x^{2}+y^{2})^{\frac{3}{2}}[/tex]

thanks.
 
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Welcome to PF

This should be posted in the "Calculus & Beyond" section of the Homework Help forum, and it should be posted using the template for homework help threads which includes:

1. An exact statement of the problem

2. Any equations that might be relevant to solving the problem

3. YOUR ATTEMPT AT A SOLUTION SO FAR

What have you done so far for this problem? Hint: can you think of a coordinate transformation that might help here?
 
I'm sorry if I was in the wrong section. I don't know about that.

I've tried using the coordinate transformation.
I suppose [tex]x^{2}+y^{2}=r^{2}[/tex]
where [tex]x=r\cos{\theta}[/tex] and [tex]y=r\sin{\theta}[/tex]

but I do not know what is the [tex]\frac{dy}{dx}[/tex]?

can you help me with this?
 
double post...
 
I was thinking you could use the chain rule ie

(dy/dx) = (dy/dr)(dr/dx)

But it's working out to be a bit messy for me. Anyway, see if that helps.
 
cepheid said:
I was thinking you could use the chain rule ie

(dy/dx) = (dy/dr)(dr/dx)

But it's working out to be a bit messy for me. Anyway, see if that helps.
i've tried it..but it just added a new problem..
[tex]r^{3}=\sin(\theta)\cos(\theta)[/tex]

then what should i do with this??
 
just develop a new equation of a circle of r^3, then write a new equation that's solvable
 

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