hi

The question in the attachment.

OK, this question will destroy my brain.

I want a start!

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- Mar 22nd 2011, 05:38 PMMissA proof concerning homogeneous DE's and integrating factors
hi

The question in the attachment.

OK, this question will destroy my brain.

I want a start! - Mar 23rd 2011, 05:34 AMAckbeet
Because the original DE is homogeneous, use one of the two standard substitutions such as $\displaystyle y=ux,$ with $\displaystyle dy=x\,du+u\,dx.$ Moreover, the following may prove useful:

$\displaystyle M(x,y)=M(x,ux)=x^{n}M(1,u),$ and the same for $\displaystyle N,$ even to the same power of $\displaystyle x,$ because of the homogeneity of the DE. Then multiply through by your integrating factor, and see if you don't see some integrable combinations pop out at you.