Difficult differential equation

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SUMMARY

The discussion focuses on solving the differential equation xy' + y = x²y². A user named Hydrolyziz seeks assistance with this equation, mentioning the unsuccessful application of the z substitution method. Another participant suggests dividing the equation by y², leading to the reformulated expression xy'/y² + 1/y = x², which facilitates further integration. This approach emphasizes the importance of manipulating the equation to simplify the integration process.

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Hydrolyziz
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Solve this differential equation:

xy'+y=x^2y^2

I've tried using the z subst. Nothing works so far. Any help would be great
 
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Welcome to PF!

Hydrolyziz said:
Solve this differential equation:

xy'+y=x^2y^2

I've tried using the z subst. Nothing works so far. Any help would be great

Hi Hydrolyziz! Welcome to PF! :smile:

(have a squared: ² :smile:)

Divide by y² to give:

xy'/y² + 1/y = x² , and carry on from there. :smile:

(Hint: if the LHS was xy'/y² - 1/y, would you be able to integrate it?

divide by some function of x so that you can use a similar method :wink:)
 

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