(a) Show that \( y_{1}(t)=\sqrt{t} \) and \( y_{2}(t)=1 / t \) are solutions of the differential equation
\[
2 t^{2} y^{\prime \prime}+3 t y^{\prime}-y=0
\]
on the interval \( 0<t<\infty \).
(b) Compute \( W\left[y_{1}, y_{2}\right](t) \). What happens as \( t \) approaches zero?
(c) Show that \( y_{1}(t) \) and \( y_{2}(t) \) form a fundamental set of solutions of (*) on the interval \( 0<t<\infty \).
(d) Solve the initial-value problem \( 2 t^{2} y^{\prime \prime}+3 t y^{\prime}-y=0 ; y(1)=2, y^{\prime}(1)=1 \).
