Verify that the indicated function

y $=($x$)$

is an explicit solution of the given first$-$order differential equation.

y$=2$xy$2$;$$y $=$

$1(16$ x$2)$

When

y $=$

$116$ x$2$

$,$

y$=$

$2$x$(16$x$2)2$

$.$

Thus, in terms of x$,$

$2$xy$2=$

$2$x$(16$x$2)2$

$.$

Since the left and right hand sides of the differential equation are equal when

$116$ x$2$

is substituted for y$,$

y $=$

$116$ x$2$

is a solution.

Proceed as in Example $6,$ by considering $$ simply as a function and give its domain. $($Enter your answer using interval notation.$)$

Then by considering $$ as a solution of the differential equation, give at least one interval I of definition.

$($$,4]$

$($$,0)$

$$

$[4,$ $)$

$(0,$ $)$

$(4,4)$