If the function f$($x$,$y$)$ is continuous near the point $($a$,$b$),$ then at least one solution of the differential equation y$^(\text{'})=$f$($x$,$y$)$ exists on some open interval I containing

the point x$=$a and, moreover, that if in addition the partial derivative $($delf$)/($dely$)$ is continuous near $($a$,$b$)$ then this solution is unique on some $($perhaps smaller$)$ interval

J$.$ Determine whether existence of at least one solution of the given initial value problem is thereby guaranteed and, if so$,$ whether uniqueness of that solution

is guaranteed.

$($dy$)/($dx$)=7$x$^(5)$y$^(4)$;y$(5)=-1$