Determine whether the Existence and Uniqueness of Solution Theorem implies that the given initial value problem has a unique solution.

$y^7\frac{dy}{dx}=x^4,y(1)=0$

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

A$.$ The theorem does not imply the existence of a unique solution because $\frac{x^4}{y^7}$ is continuous but is not continuous in any rectangle containing the point $($Type an ordered pair.$)$

B$.$ The theorem implies the existence of a unique solution because $\frac{x^4}{y^7}$ and $\frac{\text{d}\text{e}\text{l}(\frac{y^7}{y^7})}{\text{d}\text{e}\text{l}\text{y}}=$ are both continuous in a rectangle containing the point $($Type an ordered pair.$)$

c$.$ The theorem does not imply the existence of a unique solution because $\frac{x^4}{y^7}$ is not continuous in any rectangle containing the point $($Type an ordered pair.$)$