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I was given a question and i am really unsure how to go about solving it. it appears to be solveable using the characteristic equation and whatnot, however i have my coeffecients in terms of the independent variable. so i am confused. the question initially asked to compute the wronskian, and it gave the solutions, then it gives initial values to solve. There's where the confusion began. I'd be grateful for some guidance please.

Solve the initial value problem

\(\displaystyle 2t^2y''+3ty'-y= 0; y(1)=2, y'(1)=1\), given that \(\displaystyle y_1(t)=\sqrt(t) \mbox{ and } y_2(t)=\frac{1}{t}\)

The question also asked to use the Wronskian to show that the two solutions are linearly independent, then said, hence, solve the ivp (given above). I calculated the Wronskian to be \(\displaystyle \frac{-3 \sqrt{t}}{2t^2}\)

(These delimiters are not working for me, they are doing their own thing. quite annoying. )

Solve the initial value problem

\(\displaystyle 2t^2y''+3ty'-y= 0; y(1)=2, y'(1)=1\), given that \(\displaystyle y_1(t)=\sqrt(t) \mbox{ and } y_2(t)=\frac{1}{t}\)

The question also asked to use the Wronskian to show that the two solutions are linearly independent, then said, hence, solve the ivp (given above). I calculated the Wronskian to be \(\displaystyle \frac{-3 \sqrt{t}}{2t^2}\)

(These delimiters are not working for me, they are doing their own thing. quite annoying. )

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