Consider the initial value problem for the function $$ given by

$=5/(+^2),(0)=1.$

$($a$)$ Find an implicit expression of all solutions $$y of the differential equation above, in the form $(,)=,$ where c collects all constant terms. $($So$,$ do not include any c in your answer.$)$

$(,)=$$($t$,$y$)=$

$($b$)$ Find the explicit expression of the solution $$y of the initial value problem above.

$()=$