Obtaining General Solution of ODE

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Homework Help Overview

The discussion revolves around obtaining the general solution for a second-order ordinary differential equation (ODE) represented as d²y/dx² = (y/x)². Participants are exploring the implications of manipulating the equation and the validity of certain transformations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster questions whether they can equate d²y/dx² to (dy/dx)², cancel the powers, and integrate directly. Some participants suggest rewriting the equation in terms of dy/dx and exploring the implications of this transformation.

Discussion Status

Participants are actively discussing the validity of different approaches to the problem, including the need to consider both positive and negative cases when rewriting the equation. There is an exchange of ideas regarding the differentiation process and the relationships between the derivatives.

Contextual Notes

There is an emphasis on ensuring clarity in the definitions and relationships between the derivatives involved, as well as the need to explore both potential solutions arising from the transformation.

Munir M
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Homework Statement


So they want me to obtain the general solution for this ODE.
Screen Shot 2016-11-01 at 12.00.43.png


Homework Equations


I have managed to turn it into d^2y/dx^2=(y/x)^2.

The Attempt at a Solution


My question is, can I simply make d^2y/dx^2 into (dy/dx)^2, cancel the power of 2 from both sides of the equation and then integrate it normally?

If not, why?
 
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I believe you can however, just make sure that you re-write it as dy/dx = +/- y/xAlso note the distinction that d^2y/dx^2 = d/dx(dy/dx) i.e. differentiating dy/dx wrt x and (dy/dx)*(dy/dx) = (dy/dx)^2.
 
rock.freak667 said:
I believe you can however, just make sure that you re-write it as dy/dx = +/- y/x
In other words, solve dy/dx = y/x as well as dy/dx = -y/x.
 
Mark44 said:
In other words, solve dy/dx = y/x as well as dy/dx = -y/x.

Thanks guys!
 

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