$$Question:Find\, \, the\, \, Wronskian\, \, of\, \, two\, \, solutions\, \, of\, \, the\, \, given\, \, differential\, \, equation\, \, without\, \, solving\, \, the\, \, equation.\\\\\\t^{2}{y}''-t(t+2){y}'+(t+2)y=0\\\\To\, \, begin\, \, with,\, divide\, \, both\, \, sides \, \, of \, \, the\, \, equation\, \, by\, \, t^{2}\\\\y{}''-\frac{t+2}{t}y{}'+\frac{t+2}{t^2}y=0\\\\Let\, \, \, \, P(t)=-\frac{t+2}{t}\\\\Then \, \, \, \, W=Ce^{-\int-\frac{t+2}{t}dt }=Ce^t\cdot e^{2lnt}=Ct^2e^t$$
