$($a$)$ Use the fact that $5x^2-y^2=c$ is a one$-$parameter family of solutions of the differential equation $y\frac{dy}{dx}=5x$ to find an implicit solution of the initial$-$value problem $y\frac{dy}{dx}=5x,y(2)=-6$

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By hand, sketch the graph of the explicit solution of this problem. Give the interval I of definition of the explicit solution for the given initial$-$value problem. $($Enter your answer using interval notation.$)$

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$($b$)$ Are there any explicit solutions of $y\frac{dy}{dx}=5x$ that pass through the origin? $($If yes, enter the explicit solutions as a comma$-$separated list. If not, enter NONE.$)$

$y=$

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