(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the equation (y^2+2xy)dx-x^2dy=0 (a) Show that this equation is not exact. b) Show that multiplying both sides of the equation by y^-2 yields a new equation that is exact. C) use the solution of the resulting exact equation to solve the origional equation. d) Were any solutions lost in the process?

2. Relevant equations

How do you show that the solution in part b is a solution to the original?

3. The attempt at a solution

answer to part b: (x+x^2y^-1=c)

I tried (y^2+2xy)dx - x^2dy=(x+x^2y^-1) and integrated both sides to get

xy^2 + x^2y - x^2y = xy+x^2 ln y

I tried solving (x+x^2y^-1=c) for x: getting x=-x^2y^-1 +c and plugging in into the original equation : (y^2+2(-x^2y^-1 +c)y)dx - (-x^2y^-1 +c)^2dy=0 and that just got me a mess. I'm not sure what else to try.

I'm not sure how to do part d, either, but I figured I needed part c first.

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# Show the Exact Differential Equation solution is also a solution to another equation

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