Chapter 4.7, Problem 28E

Let $y_1\left(t\right)=t^2$ and $y_2\left(t\right)=2t\left|t\right|$. Are $y_1$ and $y_2$ linearly independent on the interval:

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

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

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

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