$y^{\text{'}}=2x{y}^2,y(0)=\frac{1}{4},$ To check if $4y-x^{2}y=1$ defines an implicit soluction do the following

Find $\frac{dy}{dx}$ from the explession $4y-x^{2}y=1$

Then Check that initiall$-$value problem is satisfied

Then specify the interval of validity

$($Do not solve this equation, the solution is already given$)$