1. The problem statement, all variables and given/known data Given [itex]y_1=x[/itex] is a solution, solve the differential equation 2. Relevant equations y''+xy'-y=0 3. The attempt at a solution Since I am given [itex]y_1=x[/itex] (is there a hotkey for adding TeX tags so I don't have to manually type these tags over and over? So tedious.) then I wish to vary a parameter A that y is multiplied by, A(x)... [itex]y_2=Ax[/itex] [itex]y_2'=A'x+A[/itex] [itex]y_2''=A''x+2A'[/itex] Plugging into the original equation, I end up with [itex]A''x+(x^2+2)A'=0[/itex] This is another differential equation, and I do not know where to go from here.