1st order circuit analysis
With the switch assumed closed for a long period, you must find the instantaneous current, \$\small i_L(t)\$, through \$\small L\$ when \$\small u(t)\$ is at a maximum value, i.e. when the current through \$\small R_3\$ is at a maximum. Also required is the value of \$\small i_G(t)\$ at the same instant. These define the initial conditions that will exist when the switch is opened.

The currents can be derived by solving the following differential equation via the IF method:
$$\small -u(t)=L\frac{di_L}{dt}+R_1i_L=(i_G-i_L)R_3 $$

or
$$\small\frac{di_L}{dt}+\frac{(R_1+R_3)}{L}i_L=\frac{R_3}{L}i_G $$

Now, the switch is opened, \$\small R_2\$ enters the arena, and a new clock starts ticking from \$\small t^{'}=0\$. A similar differential equation to the above may be derived, and solved to give the required unknowns.