\(y'+2xy=4x\)

\(y'=4x-2xy\)

\(dy/dx= x(4-2y)\)

\(dy/(4-2y)= xdx\)

\(int dy/(4-2y)= int xdx\)

\((ln(4-2y))/-2= x^2/2+C\)

\(ln(4-2y)= -(x^2+2C)\)

\(4-2y= e^(-(x^2+2C))\)

\(y=(4-e^(-(x^2+2C)))/2\)

\(y'=4x-2xy\)

\(dy/dx= x(4-2y)\)

\(dy/(4-2y)= xdx\)

\(int dy/(4-2y)= int xdx\)

\((ln(4-2y))/-2= x^2/2+C\)

\(ln(4-2y)= -(x^2+2C)\)

\(4-2y= e^(-(x^2+2C))\)

\(y=(4-e^(-(x^2+2C)))/2\)