Consider the following.

$y^{\text{'}}=\frac{-1x}{(2+2y)},y(0)=3$

$($a$)$ Find the solution of the given initial value problem in explicit form.

$y(x)=$

$$

$($b$)$Determine $($at least approximately $-$ use at least $4$ decimal places if using decimals$)$ the interval in which the solution is defined. $($Enter your answer using interval notation.$)$

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