The book only has one example of this and it's really confusing me.(adsbygoogle = window.adsbygoogle || []).push({});

[tex](x^2+y^2)dx+(x^2-xy)dy=0[/tex]

I can see that it's homogeneous of degree 2

They then let [tex]y = ux[/tex]

From there they state that [tex]dy = udx+xdu[/tex] (I'm not sure where this is coming from, but can just accept it on faith if I have to)

I'm fine with making the subs.

[tex](x^2+u^2x^2)dx+(x^2-ux^2)(u dx+x du)=0[/tex]

This is the part that really screws me up.

[tex]x^2(1+u)dx+x^3(1-u)du=0[/tex]

Where did the [tex]x^3[/tex] come from? All I see is [tex]x^2[/tex]. Or I guess I should ask, how did [tex]udx+xdu[/tex] become just [tex]xdu[/tex]? That would explain the [tex]x^3[/tex] they have.

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# Homework Help: Solving a homogeneous diff eq

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