$(21$ pts$)$ Solve the following initial value problems

$($a$)t^2{y}^{\text{'}}=ty4,y(1)=0,$

$($b$)y^{\text{'}}=\frac{y^{2}1}{(t1)y},y(0)=2,$

$($c$)y^{\text{'}}=4y^2-1,y(0)=-2.$