Gen Solution of 1st Order DE

[jenn9580]

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I need to determine if this is an exact DE & find a general solution.
I found that this is not an exact DE since -x/y^2 does not equal 1/x. I now need to find a general solution but I am stuck. What should I try next?

 

[tutor_joel]

The general solution to a differential equation must satisfy both the homogeneous and non-homogeneous equations. If you find a particular solution to the non-homogeneous equation, you can add the homogeneous solution to that solution and it will still be a solution since its net result will add to zero. A solution can be formed as the sum of the homogeneous and non-homogeneous solutions, and it will have a number of arbitrary (undetermined) constants. Such a solution is called the general solution to the differential equation.

do you know how to find the homo and heterogeneous solutions? This may help

 

[jenn9580]

Thanks. Just got an email from my professor saying there was a typo & the equation is y/x instead of x/y. This makes it an exact DE, which I can solve no problemo! Thanks for the info!

 

[tutor_joel]

ok, I thought that equation looked strange, I had trouble with it as well