Question

кто владеет ВЫСШЕЙ МАТЕМАТИКОЙ умоляю хелп!!!)))
Y'=y2/x2+y/x+2

Answer 1

$y'=(frac{y}{x})^2+frac{y}{x}+2\\t=frac{y}{x},y=ux,y'=u'x+ux'=u'x+u; ; (x'=1)\\u'x+u=u^2+u+2\\u'x=u^2+2\\u'=frac{du}{dx}=frac{u^2+2}{x}\\frac{du}{u^2+2}=frac{dx}{x}$

$frac{1}{sqrt{2}}arctgfrac{u}{sqrt2}=ln|x|+C\\frac{1}{sqrt{2}}fractgfrac{y}{sqrt{2}x}=ln|x|+C$