Chapter 4 - Higher Order Linear Equations - 4.1 General Theory of nth Order Linear Equations - Problems - Page 225: 24

$W(t)=\frac{C}{t}$

We will use Abel's formula to find wronskian ${y}''''+\frac{t}{t^2}{y}'''+\frac{1}{t^2}{y}'-\frac{4}{t^2}y=0\\\\$ $p_{1}(x)=\frac{t}{t^2}\;=\;\frac{1}{t}\;\;\;\;$ coefficient of ${y}'''\\\\$ $W(t)= Ce^{-\int p_{1}(x)dx}\;=\;Ce^{-\int (\frac{1}{t})dx}\;=Ce^{-ln|t|}\;=Ce^{ln\frac{1}{t}}\\\\$ $W(t)=\;C.\frac{1}{t}\;=\;\frac{C}{t}$