Question

Найдите общие решения уравнений

Answer 1

$dfrac{dy}{dx}=x(1-y)\ int dfrac{dy}{y-1}=-int xdx\ ln|y-1|=-dfrac{x^2}{2}+C_1\ |y-1|=C_2e^{-dfrac{x^2}{2}}\ y=1+Ce^{-dfrac{x^2}{2}}$

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$y'-dfrac{2y}{x+1}=(x+1)^2\ y'*dfrac{1}{(x+1)^2}+y*(-dfrac{2}{(x+1)^3})=1\ left[(dfrac{1}{(x+1)^2})'=dfrac{-2}{(x+1)^3}right]\ (y*dfrac{1}{(x+1)^2})'_x=1\ y*dfrac{1}{(x+1)^2}=x+C\ y=(x+C)(x+1)^2$