Question

Решите:
y`+$frac{y}{x}$=1

Answer 1

$y'+frac{y}{x}=1\\frac{y}{x}=t,; y=tx,; y'=t'x+t; ; ; ; ; (x'=1)\\t'x+t+t=1\\t'x=1-2t\\t'=frac{dt}{dx}=1-2t\\int frac{dt}{1-2t}=int dx\\-frac{1}{2}ln|1-2t|=x+C\\-frac{1}{2}ln|1-2frac{y}{x}|=x+C$