\(\frac{dy}{dx} - \frac yx = \frac{x+1}x\)
\(I.F.=e^{\int \frac{-1}xdx} = e^{-\log x} = \frac 1x\)
\(y(I.F.) = \int \frac{x+1}x \times I.F. dx\)
⇒ \(\frac yx = \int \frac {x+1}x \times \frac 1x dx = \int \frac{x + 1}{x^2} dx\)
⇒ \(\frac yx = \frac 12 \log x^2 - \frac 1x C\)
⇒ \(y = x\log x - 1 + Cx\)
which is general solution of given differential equation.
