Finding the total energy of the network in steady state
HINT

In DC steady state, the voltage at the top of the 5V supply and the top of the 4 ohm resistor will be the same.  Then your circuit just looks like this:







simulate this circuit &ndash; Schematic created using CircuitLab

Use Thevenin's theorem to simplify the voltage divider on the left hand side, and you'll get a circuit containing just a voltage source, a current source, an inductor, and resistor.  The current through L1 will be 6A, so you can calculate the energy in that inductor.  The same current must flow into the Thevenin equivalent voltage source, so you can easily find the current through the first inductor by equating powers: \$V_{th}*6A = 5*I\$ and solving for I.  This will be the current through the first inductor.  The voltage across the capacitor in steady state will be 5 volts, so you know the energy in it.  Add them up to get the total energy in the circuit.