Intro Circuits Class Inductor question
Since this is homework, I won't solve this completely for you, but I'll show you how to set up the equations:

First question "a". Let's name the bottom node "ground", and the top node "node 1", and call its voltage "v1". Now for each of the elements you can write a branch equation:

\$\dfrac{\mathrm{d}i_1}{\mathrm{d}t} = -\dfrac{v_1(t)}{3H}\$ (\$i_1\$ directed opposite of passive reference convention)

\$\dfrac{\mathrm{d}i_2}{\mathrm{d}t} = \dfrac{v_1(t)}{6H}\$

\$i_R(t) = \dfrac{v_1(t)}{2\Omega}\$

You also have a node equation for node 1:

\$i_1(t) = i_2(t) + i_R(t)\$

Given the initial conditions, you can also work out that the resistor current at t=0 is -1 A, and so \$v_1(0) = -1A \cdot 2 \Omega = -2V\$ 

From here you should be able to work out a solution for the different currents over time. Since you only have one storage element (the two inductors in parallel are equivalent to a single inductor with 6*3/(6+3) = 2 H inductance), you'll most likely end up with v1(t) decaying exponentially, and then being able to work out the individual inductor currents from there. 

For equation (b), follow the same method: write all the independent branch and node equations you can, then combine and simplify until you have a solvable set of equations.