Author Topic: TUT 0702 QUIZ3  (Read 246 times)

Kunpeng Liu

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TUT 0702 QUIZ3
« on: October 11, 2019, 02:00:02 PM »
$$Question:Find\, \, the\, \, Wronskian\, \, of\, \, two\, \, solutions\, \, of\, \, the\, \, given\, \, differential\, \, equation\, \, without\, \, solving\, \, the\, \, equation.\\\\\\t^{2}{y}''-t(t+2){y}'+(t+2)y=0\\\\To\, \, begin\, \, with,\, divide\, \, both\, \,  sides \, \, of \, \, the\, \,  equation\, \,  by\, \,  t^{2}\\\\y{}''-\frac{t+2}{t}y{}'+\frac{t+2}{t^2}y=0\\\\Let\, \, \, \,  P(t)=-\frac{t+2}{t}\\\\Then \, \, \, \, W=Ce^{-\int-\frac{t+2}{t}dt }=Ce^t\cdot e^{2lnt}=Ct^2e^t$$