Chapter 6.1, Problem 1E

In Problems $1-6$, determine the largest interval $\left(a,b\right)$ for which Theorem $1$ guarantees the existence of a unique solution on $\left(a,b\right)$ to the given initial value problem.

$x{y}^{‴}-3y^{\prime }+e^{x}y=x^2-1$;

$y\left(-2\right)=1$, $y^{\prime }\left(-2\right)=0$, $y^{″}\left(-2\right)=2$