Substitution for integration of e^(x*y) dx

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Homework Help Overview

The discussion revolves around finding an appropriate substitution to simplify the integration of the expression e^(x*y) within the context of a differential equation involving the terms x(dy/dx) + y = e^(x*y).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are exploring potential substitutions for the integration of e^(x*y) and questioning the implications of their choices, particularly regarding the complexity introduced by multiple instances of (x*y).

Discussion Status

The discussion is ongoing, with participants raising questions about derivatives and substitutions. Some guidance has been offered regarding the derivative of the product xy, but no consensus or clear direction has emerged yet.

Contextual Notes

There appears to be a concern about the complexity of the expression after substitution, and participants are navigating the implications of their proposed approaches without a definitive resolution.

Sunev
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Really not sure... Does anyone know an appropriate substitution?

The whole problem is:

Find the substitution that simplifies the differential equation

x(dy/dx) + y = e^(x*y)
 
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What is
\frac{d(xy)}{dx}
?
 
I know the first part. It is the integration of e^(x*y) that I am having problems with, as it requires a substitution...
 
don't you think that afterwards you will have too many (x*y)s?

one more sentence and the other party will have to solve it -_-
 
Sunev said:
I know the first part. It is the integration of e^(x*y) that I am having problems with, as it requires a substitution...
I understand that- and if you had answered my question, it should have become obvious to you what substitution you need.
 

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