y^{\prime}-y\frac{2x-1}{x^2}=1\\
y^{\prime}-y\frac{2x-1}{x^2}=0\\
y^{\prime}=y\frac{2x-1}{x^2}\\
\frac{\mbox{d}y}{\mbox{d}y}=y\frac{2x-1}{x^2}\\
\frac{\mbox{d}y}{y}=\frac{2x-1}{x^2}\mbox{d}x\\
\ln{|y|}=2\ln{x}+\frac{1}{x}+C\\
y=Cx^2e^{\frac{1}{x}}\\
y\left(x\right)=C\left(x\right)x^2e^{\frac{1}{x}}\\
C^{\prime}\left(x\right)x^2e^{\frac{1}{x}}+\left(2x-1\right)C\left(x\right)-\left(2x-1\right)C\left(x\right)=1\\
C^{\prime}\left(x\right)x^2e^{\frac{1}{x}}=1\\
C^{\prime}\left(x\right)=\frac{1}{x^2}e^{-\frac{1}{x}}\\
C\left(x\right)=e^{-\frac{1}{x}}+C\\
y=x^2e^{\frac{1}{x}}e^{-\frac{1}{x}}+Cx^2e^{\frac{1}{x}}\\
y=x^2\left(1+Ce^{\frac{1}{x}}\right)