\displaystyle yy'=2y-x\\
z=\frac{y}{x}\\
z+xz'=y'=2-\frac{1}{z}\\
\frac{dz}{2-\frac{1}{z}-z}=\frac{dx}{x}\\
-\frac{1}{2}\frac{2\left( z-1\right)dz}{\left( z-1\right)^2}+\frac{dz}{\left( z-1\right)^2}=\frac{dx}{x}\\
-\frac{1}{2}\int\frac{2\left( z-1\right)dz}{\left( z-1\right)^2}+\int\frac{dz}{\left( z-1\right)^2}=\int\frac{dx}{x}\\
-\frac{1}{2}\ln|\left( z-1\right)^2|-\frac{1}{z-1}=\ln|x|+\ln C\\