$(30$ points$)$ Solve the following recurrences. You must show the steps of solving recurrence.

You may not use the Master Theorem.

$T(n)=T(\frac{n}{5})+cn,T(1)=1$

$T(n)=4T(\frac{n}{3})+c{n}^2,T(3)=1$

$T(n)=16T(\frac{n}{2})+n^3,T(1)=1$