Use the method of reduction of order to find a second independent solution of the given differential equation. t2y'' + 3ty' + y = 0, t > 0; y1(t) = t−1

I assume you mean , and not , since this doesn't satisfy the ODE.

Assume a second solution of the form , where is a function of . Then

Substituting into the ODE gives

where we omit the second term because it's already accounted for by .

answer: the answer is ann