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## Homework Statement

Solve by making an appropriate substitution. I am given the homogeneous DE:[tex]xdx+(y-2x)dy=0[/tex]

Now we have bee using either y=ux or x=vy. . . I tried both, but the latter seemed easier.

[tex]x\frac{dx}{dy}+y-2x=0[/tex] letting x=vy and dx/dy=v+y*dy/dv

[tex]vy(v+y\frac{dy}{dv})+y-2vy=0[/tex]

[tex]v^2+y^2\frac{dy}{dv}+y-2vy=0[/tex]

Here is where I get stumped. . . this is supposed to be separable now right? Because I can't seem to see it.

A hint would be swell!

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