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6. y+xy'=3y²y', y(1)=1

y+xdy/dx=3y²dy/dx, ydx/dy+x=3y², yx'+x=3y²
x'+x/y=3y, x=Ce^-∫dy/y=Ce^-lny=C/y
x=C(y)/y, (C(y)/y)'+C(y)/y²=3y, (C'(y)y-C(y))/y²+C(y)/y²=3y
C'(y)/y=3y, C'(y)=3y², C(y)=∫3y²dy=y³+C₁
x=(y³+C₁)/y
y(1)=1, 1=(1+C₁)/1, C₁=0
x=y²