How to solve Steps for The inital value problem

You are working in a group using high powered lasers to create nuclear fusion. One proposal is to supply the energy to the lasers using an inductive circuit, as shown in the diagram. When the switch is at position $1,$ the inductor is energized by the DC power source with emf $.$ The internal resistance of the power supply is represented by the small resistor with resistance $r.$ When the inductor is fully energized, the switch flips to position $2$ and the inductor transfers its energy to the laser, modeled as the resistor $R_L.$

Your group leader is concerned that the self$-$inductance of the inductor will prevent the energy stored in it from being transferred to the laser quickly enough. You have been asked to calculate how long it takes after moving the switch to position $2$ for the inductor to transfer $90\%$ of its energy to the laser $($dissipated in the equivalent resistor$)$ in terms of the values of the circuit components.