How can I integrate x^3/y^2 to solve this differential equation?

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Homework Help Overview

The discussion revolves around solving a differential equation of the form dy/dx = x^3/y^2, with an initial condition y(2) = 3. Participants are exploring methods of integration and separation of variables in the context of differential equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the possibility of separating variables to facilitate integration. There is a question about the correctness of the separation process and the resulting equation. Some participants seek clarification on the integration steps and the implications of the initial condition.

Discussion Status

There is an ongoing exploration of the separation of variables approach, with some participants suggesting methods for integration. Guidance has been offered regarding the integration process and the importance of the initial condition in determining the constant of integration. Multiple interpretations of the separation process are being considered.

Contextual Notes

Participants are working within the constraints of needing to integrate the expression and apply the initial condition, while also questioning the correctness of their algebraic manipulations.

Pseudo Statistic
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How can I find the solution to this differential equation: dy/dx = x^3/y^2 given y(2) = 3?
I'd just like a hint on how I can integrate x^3/y^2... because that's where I'm falling.
Thanks for any responses.
 
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Can you not separate the equation and then integrate?
 
When I separate, do I get:
x^3dx - y^2dy = 0?
Or is this wrong?
I was asking to check..
Thanks.
 
Pseudo Statistic said:
When I separate, do I get:
x^3dx - y^2dy = 0?
Or is this wrong?
I was asking to check..
Thanks.

That's fine- although you might find it simpler yet to write the equation as
x3dx= y2dy

Now integrate both sides. You get a "constant of integration" when you do that. Remember that y(2)= 3 means that when x= 2, y= 3. That will help you determine what that constant must be.
 

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