Chapter 4.7, Problem 26E

Let $y_1\left(t\right)=t^3$ and $y_2\left(t\right)=\left|t^3\right|$. Are $y_1$ and $y_2$ linearly independent on the following intervals?

$\text{a}$. $[0,\infty )$

$\text{b}$. $(-\infty ,0]$

$\text{c}$. $\left(-\infty ,\infty \right)$

$\text{d}$.Compute the Wronskian $W\left[y_1,y_2\right]\left(t\right)$ on the interval $\left(-\infty ,\infty \right)$.