$\frac{dy}{dx}=8x^6{y}^2$;$y(7)=-5$

Select the correct choice below and fill in the answer box$($es$)$ to complete your choice.

$($Type an ordered pair.$)$

A$.$ The theorem implies the existence of at least one solution because $f(x,y)$ is continuous near the point $$ This solution is unique because $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}=$ is also continuous near that same point.

B$.$ The theorem implies the existence of at least one solution because $f(x,y)$ is continuous near the point $$ However, this solution is not necessarily unique because $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}=$ is not continuous near that same point.

C$.$ The theorem does not imply the existence of at least one solution because $f(x,y)$ is not continuous near the point