Problem $1$: $(3$ points, $1$ point each$)Do$ the following ODE satisfy

the assumptions $of$ the Existence$-$Uniqueness Theorem from lecture?

Why $or$ why not?

$(a)$

$\frac{dy}{dt}=\frac{y}{t^2+1}$

$y(-1)=9$

$(b)$

$\frac{dy}{dt}=y^2(|t|+y)$

$y(0)=2$

$(c)$

$\frac{dy}{dt}=\frac{1}{y+1}$

$y(1)=-1$