How to analyze RL circuit with sequential switching?
for t&lt;0 you have this circuit :







simulate this circuit &ndash; Schematic created using CircuitLab

first, you should calculate IL for t&lt;0:
  

When SW1 move from a to b we have this circuit:







simulate this circuit









simulate this circuit

the equivalent resistor of 5 and 20 ohm is 4 So you have :







simulate this circuit



to obtain voltage equation we derivate the current equation: