So I just started my DE class and I'm kinda stuck on solutions by substitutions. My book explains it as just having a homogeneous function of degree α, we can also write M(x,y) = x(adsbygoogle = window.adsbygoogle || []).push({}); ^{α}M(1,u) and N(x,y) = x^{α}(1,u) where u = y/x

I don't understand how the substitution simplifies our life ( there's no proof in my book , it just says that a function can have y = g(x,u) and replace g(x,u) in f(x,y)). To me it seems more complicated than anything.

Secondly, how do I find my x^{α}. I tried doing many examples, but without success I never get the correct coefficient, so there is something I'm not understand. I just have to factor out the highest degree of x, no?

Any help would be greatly appreciated

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# Can't understand solution by substitution, any help?

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