Help me solve this optional problem and show all work done and label if you can, thank you.

Homework: Separable Equations

Sonsider the initial value problem for the function $y$ given by

$y^{\text{'}}=\frac{5t}{(y+y{t}^2)},y(0)=1$

$($a$)$ Find an implicit expression of all solutions $y$ of the differential equation above, in the form $(t,y)=c,$ 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.

$y(t)=$

$$