\((dy/dx)+(1/x)y = 6x + 2\)

Now, compare with \(dy/dx+Py=Q\), we get

\(P=1/x\text{ and }Q= 6x+2\)

\(I.F. = e^{\int(1/x dx)}\)

\(= e^{(\ln x)}\)

= x

\(y*x= \int (6x+2)x dx\)

\(xy= \int 6x^2*dx+\int 2x*dx\)

\(xy= 2x^3+x^2+C\), where C is a constant

\(dy/dx+(1/x)y= 6x+2\text{ is }xy= 2x^3+x^2+C\)