Another Separable Differential Equation

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Homework Help Overview

The discussion revolves around solving a separable differential equation of the form x²y²y' + 1 = y. Participants are exploring methods to integrate the expression on the right-hand side after separating variables.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • One participant has attempted to separate variables and reached a point involving an integral of the form int(y²/(y-1))dy. Others suggest polynomial division as a potential method for simplifying the integral. There is also a suggestion to use u-substitution with u = y - 1, which raises questions about the implications of changing variables.

Discussion Status

The discussion is active, with participants offering different approaches to tackle the integral. There is no explicit consensus on the best method yet, but various strategies are being explored, including polynomial division and substitution techniques.

Contextual Notes

Participants are navigating the complexities of integrating a rational function, with some expressing uncertainty about the integration process and the implications of their chosen methods.

crm07149
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Homework Statement


Solve the following equation by separating variables.

Homework Equations


x2y2y' +1 = y

The Attempt at a Solution


I have been able to work through the problem to this point:

-1/x + C = int(y2/y-1)dy

I am not sure how to integrate the right hand expression int(y2/y-1)dy
 
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Polynomial division of y2/(y-1) looks like it will work.
 
Last edited:
Have you tried u-substitution with u=y-1?
 
What do you mean by polynomial division?

u-substitution with u = y-1 brings it to int(y^2/u)du, with both y and u variables
 

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