For the linear differential equation y$+6$xy$=$x$^2*$ e$^6$x$^2/2$ the integrating factor is:r$($x$)=$

e$3$x$2$

help $($formulas$)$After multiplying both sides by the integrating factor and "unapplying" the product rule we get the new differential equation:ddx$[$

e$3$x$2$y

$]=$ help $($formulas$)$Integrating both sides, we get the algebraic equation$=+$C

help $($formulas$)$Solving for y$,$ the general solution to the differential equation isy$=$ help $($formulas$)$Note: Use C as the constant.