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I have first-order differential equation $$y=xy'+ \frac{1}{2}(y')^{2}$$ Maybe, with this someone will find way to solve it $$\frac{1}{2}y'(2x+y')=y$$ I thought I can use $x^2+y=t$ for subtitution and when I derivate, I have $t'=2x+y'\\(t'-2x)t'=2t-2x^2$ which is acctualy the same as previous. I don't have idea how to start..