In this problem, $y=\frac{1}{x^2+c}$ is a one$-$parameter family of solutions of the first$-$order DE $y^{\text{'}}+2x{y}^2=0.$ Find a solution of the first$-$order IVP consisting of this differential equation and the given initial condition.

$y(-3)=\frac{1}{4}$

$y=$

Find the domain of $y$ considered as a function over the reals. $($Enter your answer using interval notation.$)$

Give the largest interval I over which the solution is defined for the given initial condition. $($Enter your answer using interval notation.$)$