Chapter 6.1, Problem 3E

Use separation of variables to find solutions of the IVP given by $y(0)=1$ and the following differential equations:

$\begin{array}{l}\text{a}\text{. }y\text{'}=t\\ \text{b}\text{. }y\text{'}=t^{2}y\\ \text{c}\text{. }y\text{'}=2(t+1)y\\ \text{d}\text{. }y\text{'}=5t^{4}y\\ \text{e}\text{. }y\text{'}=1/y^2\\ \text{f}\text{. }y\text{'}=t^3/y^2\end{array}$