Attempt $3$: $18$ attempts remaining.

Consider the initial value problem

$y^{\text{'}}-5y=10t+2e^t,y(0)=y_0$

$($a$)$ Solve the initial value problem. $($enter yo for $y_0).$

$y(t)=$

$$

$($b$)$ Determine the value of $y_0$ that separates solutions that grow positively as $t$ from those that grow negatively.

$y_0=$

$$